Are US detention centers on the US-Mexico border "concentration camps"?

The way you phrased the question makes it a political one, hinging on what one deems "insufficient facility"--a slippery slope in a game of moving the goal post.

Had you asked instead whether concentration camps are understood to include those prison jail detention halls, then the descriptive answer depends on a bunch of criteria. Trivially, since "concentration camp" is markedly applied to Nazi's death camps, and it lies near that the allusion is intended here as exegaration, the usage can as well be treated as a matter of rhetorics. This can become lexicalized, but it is here to stay depends on who wins the debate.

As definitions depend on context, within the narrow context that you have pointed at, the dictionary has no authority, so there is no either-or. That would be pre- or proscriptive.

In U.S. English, "concentration camp" has an array of potential meanings. People have applied it variously to what might be termed "forced-labor camps," such as those in the Soviet gulag; to the "death camps" under Nazi control; to the "reeducation camps" of Vietnam in the immediate post–Vietnam War era; and to "internment camps" such as those used to confine U.S. citizens of Japanese descent during World War II. One might also use it to describe refugee camps, resettlement camps, prisoner-of-war camps, and other forms of mass incarceration. Ultimately, it's a very broad, vague term.

Objectively, what one can say about the term is that it has gone through some changes since it first began appearing in dictionaries. It may be of interest to look at how Merriam-Webster has defined the term in successive editions of its Collegiate Dictionary series, starting with this entry in the "New Words" section of Webster's Fifth Collegiate Dictionary of 1944 (there was no entry for "concentration camp" in the original [1936] version of the Fifth Collegiate, nor in versions published at least as late as 1941):

concentration camp. A military camp in which troops are temporarily concentrated; also, a detention camp in which prisoners of war, political prisoners, foreign nationals, refugees, and the like, are confined.

From Webster's New [Sixth] Collegiate Dictionary (1949):

concentration camp. 1. A military camp in which troops are temporarily concentrated. 2. A detention camp in which prisoners of war, political prisoners, foreign nationals, refugees, and the like, are confined.

From Webster's Seventh New Collegiate Dictionary (1963):

concentration camp n : a camp where persons (as prisoners of war, political prisoners, or refugees) are detained or confined

Merriam-Webster's Eighth Collegiate Dictionary (1973): no change in the definition.

Merriam-Webster's Ninth Collegiate Dictionary (1983): no change in the definition, but MW added a first occurrence date of 1901 to the entry.

Merriam-Webster's Tenth Collegiate Dictionary (1993): no change in the definition.

Merriam-Webster's Eleventh Collegiate Dictionary (2003): no change in the definition.

Merriam-Webster's full-size dictionary, Webster's Third New International Dictionary (1986) has a somewhat longer entry for the term:

concentration camp n : a camp where persons (as prisoners of war, political prisoners, refugees, or foreign nationals) are detained or confined and sometimes subjected to physical and mental abuse and indignity

And finally, from Merriam-Webster Online:

concentration camp noun : a place where large numbers of people (such as prisoners of war, political prisoners, refugees, or the members of an ethnic or religious minority) are detained or confined under armed guard —used especially in reference to camps created by the Nazis in World War II for the internment and persecution of Jews and other prisoners

To summarize, back in 1944 Merriam-Webster seems to have believed—mistakenly, as it turns out—that "concentration camp" originally referred to a mustering site for military deployment, and some time later to have referred to an area designed to hold masses of people confined for any of various reasons. Only within the past 16 years has MW noted that the term may be "used especially in reference to camps created by the Nazis in World War II for the internment and persecution of Jews and other prisoners."

I have heard "concentration camp" used since the early 1960s specifically in connection with the Nazi camps, but I have also heard it used in connection with the other types of camps noted in the first paragraph of this answer. Evidently, the term is sufficiently unsavory that government entities around the world are eager to use different names to describe their camps: "processing facilities," "holding areas," etc. But the broad language of Merriam-Webster's definition of the term (published as recently as 2003) suggests that any detention camp designed to confine "prisoners of war, political prisoners, foreign nationals, refugees, and the like" can properly be termed a concentration camp.

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Early instances of 'concentration camp': Spanish policy in Cuba, 1897–1898

The earliest matches for "concentration camp[s]" are from 1897, in connection with Cuba, just prior to the advent of the Spanish-American War of April–August 1898. From "Facts About Cuba: Pacification Which Holds Good Until Sunset," in the Aspen [Colorado] Daily Times (May 16, 1897), reprinted from "Correspondence of the [St. Louis, Missouri] Globe-Democrat":

There are small towns in Matanzas where the same energy of destruction has been at work that is seen at the railroad towns. These were towns of solid built stone houses and tiled roofs. They were not large enough for the Spanish to garrison them or for the inhabitants to volunteer a sufficient force to defend them. The insurgents came down upon them and if they did not leave them ["]not one stone upon another," it was because they found the task of battering down the walls too fatiguing. ... These wrecked towns are abandoned. Trains stop at them no more. The former inhabitants have been driven to the nearest concentration camp and occupy guano huts made of poles and leaves of the savanna palms instead of their former substantial houses. Without the actual sight, it is difficult to form any conception of the fury of this destruction.

From "One Way to Aid Cuba: United States Should Make an Official Investigation," in the Macomb [Illinois] Journal (May 27, 1897), reprinted from the St. Louis [Missouri] Globe-Democrat:

The administration and congress at Washington may be informed easily and quickly as to the operation of the Spanish policy of concentration. Cabled instructions to the consuls will obtain this information in official form. They will show the magnitude of this herding of the agricultural population of four provinces in camps, the failing food supply, the demoralization, the sickness, the mortality. ... If the files of the state department are examined, it may be found that several American consuls in Cuba, without waiting to be told, have been prompted by a sense of duty to humanity to report on the concentration. But the situation grows worse week by eek, and what was true to months ago must be multiplied to make up the present total of misery. ...Smallpox is ravaging some of these camps. Yellow fever is spreading in many of them. Typhus has made its dreaded appearance. If the investigation cover the whole island, the differences in the tenor of the reports from the four pacified provinces and from the two where concentration has made no progress will afford significant contrast.

It is safe to say that there will be but one consular district in the four provinces of Pinar del Rio, Havana, Matanzas and Santa Clara from which the report will not be appalling, if consuls write as they talk. In the Cienfuegos district Consul McGarr does not believe that the concentration has wrought much hardship to the pacificos. He admits, however, that he knows little of conditions outside of the city of Cienfuegos, which is strongly Spanish in sentiment, and has been favored in the execution of the order as has no other city outside of Havana. If Consul McGarr will visit Palmiras, Cruces and concentration camps within two hours' ride of Cienfuegos, he will have some of the distressful scenes to write about.

From "Depopulating Cuba," in the [Bloomington, Illinois] Weekly Pantagraph (June 18, 1897), reprinted from the St. Louis [Missouri] Globe-Democrat:

As far as Gen. [Valeriano] Weyler's policy for the future is indicated by his military orders for the last six months it is to compel the inhabitants of the interior of the island either to go to his concentration camps, or to be placed on the footing of insurgents, and treated accordingly. This line of action is to be pursued regardless of age or sex, and is a declaration of war against the whole body of the people, non-combatants as well as those capable of bearing arms. Cromwell tried a similar plan in Ireland. He drove the native Irish into the poorest fourth of the island and divided the other three-fourths among his soldier.

Weyler was the Spanish Governor-General of Cuba from January 1896 through October 1897. Interestingly, the Wikipedia article about Weyler says that he "learned that tactic [of dividing territory to be pacified into sectors and relocating the inhabitants into areas near cities] from studying William Tecumseh Sherman's campaign" during the U.S. Civil War. In any event the correspondent for the St. Louis Globe-Democrat sees a similar antecedent in Cromwell's 1649–1653 campaign in Ireland.

From an untitled news brief in the [Terre Haute, Indiana] Semi-Weekly Express (June 22, 1897):

Premier Canovas goes on talking about reforms in Cuba and Weyler continues to increase the number of his concentration camps.

Antonio Cánovas del Castillo was the Spanish premier in Cuba. A Cuban "anarchist" assassinated him less than two months after this news item appeared.

From an untitled news brief in the Blue Mound [Illinois] Leader (July 22, 1897):

Gen. Weyler says his first thought always is the glory of Spain. A photograph of one of his concentration camps is the most horrible definition of glory yet invented.

From "Spain and Her Colonies," in the [Bloomington, Illinois] Weekly Pantagraph (September 17, 1897), reprinted from the St. Louis [Missouri] Globe-Democrat:

As far as the news from Cuba can be sifted, the tide has turned against the latest and worst of Gen. Weyler's plans of campaign. His concentration camps, where the rural population, men, women and children are huddled in order to be under military observation, have served to strengthen the insurgent armies in numbers as well as well as purpose. In those camps of famine and pestilence men who have been non-combatants see their families perishing day by day and take the first chance to join the Cuban forces.

From an untitled news brief in the [Santa Cruz, California] Evening Sentinel (January 5, 1898):

The death rate in Cuba is very high, and the Spanish army suffers with the natives. Pestilence bred, in the concentration camps is no respecter of army lines.

From Charles Pepper, "Dying of Hunger: Relief for Starving Cubans by no Means Sufficient," in the [Washington D.C.] Evening Star (February 18, 1898):

Traveling, however, is less harrowing to the traveler. In half a dozen trips, I have not made one in which the begging was so little obtrusive as now. To a person making the journey for the first time, it might seem a terrible exhibition of the condition to which the country has been reduced. Not so to one who has been over the ground previously. I have seen the concentration camps as populous as a crowded city. It has been my experience to see these people drawn up in double file along the railroad tracks, old men, women with puny children at their breasts, half-clad girls, young boys, stretching forth bony hands and struggling like starved wild cats for the alms which might be tossed them by the compassionate stranger. That sight is no longer witnessed. While the scenes of individual suffering are such that a traveler would gladly close his eyes to them, the beggars no longer surround the trains and besiege the travelers in a mass. The grave has claimed so many that a mass meeting of reconcentradoes at any one point would not be possible. Hundreds of the bohios, or palm huts, in which they were huddled, are now tenantless.

...

What remain of the country people are still kept in the concentration camps and in the villages. The military authorities continue to nullify the effort to put them back in their homes in the country.

From "Why Cuba Should Be Free" in The Dalles [Oregon] Times-Mountaineer (March 26, 1898):

Never again can Cuba be tranquil under a European sovereignty. It has fought too many wars for freedom and suffered too deeply to acknowledge once more the flag of Spain. Many of the insurgents in the field have witnessed the desolation of their homes and heard from the concentration camps of the death of their families. No American can ask them to forgive the past, accept deceitful pledges, and embrace anew the oppressor and his armed sovereignty.

The most striking thing about the articles that mention concentration camps in the year running up to the start of the Spanish-American War on April 21, 1898, is the shift in tone of the news reports reaching U.S. newspaper. The first report (from May 16, 1897), which like several others seems to have been the work of the same foreign correspondent writing for the St. Louis Globe-Democrat treats the concentration camps as places of refuge for noncombatants from the depredations of the Cuba Libre insurgents. But just ten days later, the Globe-Democrat published an account of the horrible conditions at the concentration camps and the cruelty of the Spanish government's concentration policy—as did all subsequent reports from Cuba before the outbreak of the war between Spain and the United States.

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Early instances of 'concentration camp': U.S. military mustering grounds, 1898

The unrelenting negativity of this line of stories makes what happened next even more surprising: U.S. newspapers began referring to the gathering grounds for U.S. military forces prior to their being sent to fight in Cuba as "concentration camps." From "Battle of Chickamauga: Reminiscences of One of the Famous Struggles of the Civil War," in the Omaha [Nebraska] Daily Bee (April 24, 1898):

The selection of the battlefield of Chickamauga, now a national cemetery and par ? , as a concentration camp for United States troops, recalls the story of the tragedy which hallowed that famous field with the life blood of thousands.

From "Two Cents a Mile No Go: Omaha and Northern Pacific Less Mercenary," in the St. Paul [Minnesota] Globe (April 30, 1898):

The fight that has been given publicity in The Globe against the proposition of the executive committee of the Western Passenger association to charge a uniform rate of 2 cents a mile per capita for the transportation of federal and state troops to the various concentration camps has had its effect, and the proposition has been knocked on the head.

From "Washington as a Military Center," in the [Washington, D.C.] Evening Star (May 9, 1898):

The national capital is grateful for the favors granted today by the military authorities in choosing in this vicinity a site for one of the concentration camps and for designating the local contingent as a regiment of infantry instead of a mere battalion, as at first proposed. These two favors are sincerely appreciated. Washington will unquestionably be found an ideal camping place for the twenty-five thousand or more volunteers forming the reserve division, while the local regiment will surely be recognized as one of the finest bodies of troops in the entire volunteer army. The decision is in accordance with the wishes and hopes of the people of the capital.

From "An Order Issued: Giving Destination of the Volunteers: Movement on Cuba: Will Not Fail for Lack of Sufficient Force," in the [Los Angeles, California] Herald (May 10, 1898):

It is the expectation that the first regiments recognized and reported from the states will be sent to Chattanooga [Tennessee], thence going to Cuba via Mobile [Alabama], Tampa [Florida], New Orleans [Louisiana] and Galveston [Texas], for expeditions will be dispatched from each of these ports. The governor of a state will have no hand in the distribution of the regiments to go to particular concentration camps; the destination will depend upon the promptness with which they volunteers are placed and are ready for duty. Probably about one-third of the entire levy called for by the president will constitute the force to be sent south to take part in the first Cuban service, following the regular army forces.

From "Death Traps," in the Scranton [Pennsylvania] Tribune (August 29, 1898):

Several reasons are pointed out in the report for the camp's unwholesomeness, all of which reflect harshly upon the judgment of those responsible for the camp's location. ... ["]The camps have been changed to new sites only to extend foulness and infection. The whole park reeks with it. It is estimated that 8,000 tons of garbage, manure and sweepings now infect it. Every precaution is being taken, but it is too late. The mischief has been done. This park, as a camping place, is incurably infected."

If such has been the sanitation of the principal concentration camp, which at the outset of the war was most highly indorsed by the medical department, It Is hardly surprising that the other camps have been even more prolific as breeding places of disease.

The U.S. and Spain had already signed a peace protocol on August 12, although the Treaty of Paris formally ending the war was not signed until December 10, 1898.

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Early instances of 'concentration camp': the Second Boer War, 1900–1901

The first Elephind match for "concentration camp" in connection with the Second Boer War in South Africa (October 1899–May 1902) appears in "Austral-Canadian March to Mafeking: How It Was Done: The Battle of Doornberg," in the [Grafton, New South Wales] Clarence and Richmond Examiner (July 17, 1900):

General Carrington, before he left Capetown, had made up his mind to send this advance force to join Colonel Plumer, and wired, and Messrs. Zeederberg, coach contractors, had all the coaches ready when the Bushies and Canadians were ready at the concentration camp on the Beira railway.

But soon enough the term was being applied to the holding facilities for relocated Boer families held under guard. From "Concentration Camp on the Rand: Burghers to Be Laagered on the Johannesburg Racecourse," in the New-York Tribune (December 8, 1900):

In pursuance of the reconcentrado policy, the authorities here are preparing accommodation on the racecourse for four thousand people from farms in the vicinity of the Rand. The burghers will be herded in a laager and will be strictly watched.

From "Miscellaneous" in the [Brisbane] Queenslander (April 27, 1901):

Replying to questions in the House of Commons [in London] last night, Mr. W. St. John Brodrlck stated that there were now 20,671 Boer refugees in the concentration camps that had been established In the Transvaal. The people in the various camps were all being rationed alike, and education was provided for the children.

And from "Treatment of Refugees: Debate in the Commons," in the [Sydney, New South Wales] Evening News (June 19, 1901):

Mr. St. John Brodrick, Secretary of State for War, in reply to a question in the House of Commons last night, said that there were 37,738 people in the refugee concentration camps in the Transvaal. This number included natives. In the Natal concentration camps there were 2524 people, in the Orange River Colony, 20,374, and in Cape Colony 2490.

Mr. David Lloyd-George, Liberal, moved the adjournment of the House to call attention to the treatment of the refugees. He complained that the refugees were not treated with consideration.

Sir H. Campbell Bannerman, leader of the opposition, said that the concentration camps were barbarous.

Mr. St. John Brodrick hotly, denied that there had been inhumanity in the treatment of the refugees in the camps. The extreme leniency that had been shown by the British had protracted the war. In the Johannesburg camp the high mortality in May was owing to an outbreak, of measles. The women during the outbreak refused to follow the dietary directions.

"Horrors of British Concentration Camps," in the Houston Daily Post (October 20, 1901), reprinted from the Pittsburgh [Pennsylvania] Dispatch paints a very different picture from the one promoted by St. John Brodrick. A followup article in the Houston Daily Post about Emily Hobhouse, "A Noble Woman" (December 21, 1901) indicates that the mortality figures in the concentration camps in October and November 1901 were appalling:

Th British government has decided to abandon the system of concentration camps in South Africa.

...

Consider the figures. In the blue book published in London on last Saturday, the October deaths in the Boer concentration camps are stated to have aggregated 3156, of whom 2633 were children; the November deaths 2807, of whom 2227 were children. Thus in two months nearly 5000 children have died in the concentration camps.

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Conclusions

The strategic policy of reconcentrado—mass detention of suspect populations within a country or other defined geographic area—didn't vanish after the Second Boer War, but the policy as practiced by the British colonial authorities during that war seems to have stigmatized the term "concentration camp" sufficiently that it became a term one would apply to other governments and their policies, not to one's own. This is probably why the U.S. policy of moving Japanese nationals and Japanese-American U.S. citizens to concentration camps during World War II referred to "internment" in "internment camps" rather than to "concentration" in "concentration camps."

It is certainly true that concentration camps historically have offered extremely varied levels of living conditions to their inmates, which has undoubtedly encouraged people who want to distance their own country's camps from some of the deadlier camps of the past to use mortality rates—or some sort of numbers-based quality of living index—to claim that their camps aren't concentration camps at all.

But the fundamental criteria that define a concentration camp have never focused on the likelihood that a detainee will die in it; rather, they have focused on (1) mass detention (2) of a particular suspect class of persons (such as prisoners of war, political prisoners, foreign nationals, or refugees) (3) in a concentrated area (4) under guard (5) with limited contact permitted with people outside the camp.

It is difficult to see how that traditional definition—still expressed in essentially those terms in the most recent Merriam-Webster's Collegiate Dictionary—would not apply to, for example, facilities along the U.S. border and in the nation's interior dedicated to confining large numbers of undocumented immigrants and asylum seekers prior to disposition of their cases.