"True" vs. "right" vs. "correct"

Words often have several — even many — meanings (polysemes) even limiting analysis to what are agreed to be usages of the same word (unlike different homonyms, bear = "animal" and bear = "carry" etc.). There can be many subtle shades of meaning and connotation.

I'd say that in your example, correct is unmarked for pragmatic comment (just as when a maths question is answered correctly); true carries fairly strong overtones of the dispelling of the assumption of a false smear campaign (ie there has been a suggestion in the media that the allegations are fraudulent); and right would be somewhere in between — but perhaps in a more informal register.

These shades of meaning are not universally carried by these words — a right-angle is no more morally acceptable than any other angle, and if a fence-post is out of true, it hasn't been dishonest. (Though it may have been lying in the garden.)

Allegations are "unsupported assertions of wrongdoing", especially in the context you've provided. They are usually considered to be true or false rather than right or wrong or correct or incorrect; however, all of those words can be used to describe them in one way or another.

Those who make the allegations often attempt to prove them true in a court of law or in the court of public opinion. Once the public or a judge or a jury has accepted them as accurate statements, they become true and are no longer allegations.

Therefore, I'd use "true" and say The allegations made against [politician] are true, if they're still being considered and debated, and "were true" if the politician is no longer alive or in office or in the country or in danger of being prosecuted for them, or if the allegations have been withdrawn because of political pressure.

My impression is that "correct" denotes accuracy, while "right" denotes more of judgment or (but not limited to, a moral call).

For example, the statement, "Two plus two equals four," is correct - it is not right, nor is it the right answer; it is the correct answer. Another example would be to say, "You are correct in your belief that the moon is not made of cheese."

An example of the correct usage (chuckle intended) of "right" would be, "It is right to help your mother to get up the stairs." Or, "The right way to handle a disagreement is with discussion, not violence."

As you can see, one denotes specific accuracy of an answer or action, and the other denotes a personal judgment.

However, the two can blur when "correct" is used to verify a judgment call that has been made. If a teacher asks the class the sum of two plus two, and no one is answering, and finally you relieve her apprehension by piping up with the correct answer, so as to keep the lesson moving forward, someone could correctly state to you, "You were right to speak up with that answer," as they are not describing your answer, which was correct, they are describing your choice to give the answer in the first place.

I hope this helps you to use "right" and "correct" correctly. Spreading this information was just the "right" thing for me to do.

Am I incorrect?

Prefer use of "correct" over "right" as "right" often carries the unconscious baggage of right wing thinking or being. This strongly implies that the overuse of "right" influences public thinking. Suggest that usage of the word "right" be limited to direction, one's rights, and political rights. As evidence consider: right-wing politics vs. correct-wing politics - one makes sense and one doesn't. Or: The right choice vs. the best choice. Or: Doing the right thing. vs. Doing it well.

Briefly, in my opinion, True is better used in True or False questions. Right is better used to show your approval of propositions. Correct is better used when the question has a single answer.