Is there a word for the person who hides truth in order to deceive?

Your example is an instance of a half-truth. Everything he said is true, but he did not tell the whole story.

A more colorful term is a white lie which is a partial truth that hides a much more serious or disturbing one. The recognized definition is that this is a lie of very little consequence told with good intentions in order to cover up a larger truth that might be hurtful.

The word obfuscate may apply here.

President Bill Clinton coined a new expression regarding questions about himself and "that woman, Monica Lewinsky," for this context. Slightly edited, it is: "Legally accurate but not volunteering information."

I will offer the term disingenuous, which is defined here as:

lacking in frankness, candor, or sincerity

For fans of Pirates of the Caribbean, Pull an Angelica. She lied to Captain Jack Sparrow by telling the truth.

Not a single word, but the closest idiom I could find is:

economical with the truth

Per Wikipedia:

Economical with the truth is popularly used as a euphemism for deceitful, whether by volunteering false information (i.e., lying) or by deliberately holding back relevant facts. More literally, it describes a careful use of facts so as not to reveal too much information.

I would argue that outright lying is not covered by the phrase. Sir Robert Armstrong famously used the phrase during the Spycatcher trial, claiming that he had not lied -- merely been economical with the truth.

Prosaically, you are being:

misleading

that is, saying no false hood but leading away from the truth that the other is searching for.

I would use the word prevaricate:

to speak falsely or misleadingly; deliberately misstate or create an incorrect impression; lie.

Another commonly used word for this same behavior is to fudge, meaning to disingenuously avoid or talk around an issue.

She implied or insinuated. Though one can imply truthful things, insinuate has a more disingenuous tone.

e.g.

If you had your accountant fill in your tax return, someone could say:

"You didn't fill in your tax returns"

Which is true, it is a fact. You didn't, your accountant did. But the statement implies your tax returns aren't filled in, which is untrue, and as such the truthful statement implies a mistruth.

To equivocate is to phrase your statement in an ambiguous way so that the listener is intentionally misled.

I think the second definition give for the word casuistry is dead on:

reasoning that is specious, misleading, or oversubtle

If the example is crucial to the word you are looking for, let's examine it a bit more closely

A: Hey, I remember that car with the scratch from the crash last week, you must be the one who caused it.

B: Are you sure? It didn't necessarily have to be me, I see a car with a scratch like this almost every day.

So, the crucial point is that 'a car' is used by B to mean 'some car'. However 'some car' in this context, as an argument that helps the statement that "it didn't have to be B" can only mean "a car that is not B's car". Therefore this is not just a deceit, I would still call this a lie (alternatively, it is a contradiction).

There are many definitions of a lie, I don't object to the one given by wikipedia

A lie (also called prevarication, falsehood) is a type of deception in the form of an untruthful statement, especially with the intention to deceive others.

Untruthful is defined as 'not honest or true' in macmillan.

Combining these two definitions it really is not crucial in the given example if the statement can be interpreted by someone as correct representation of reality; what is important is that the statement is not honest and has an intention to deceive. (However, I tried to show in the opening paragraph that the argument can not even be taken as something based on truth).

Wikipedia entry on deceit has the following categories:

• Lies: making up information or giving information that is the opposite or very different from the truth.
• Equivocations: making an indirect, ambiguous, or contradictory statement.
• Concealment: omitting information that is important or relevant to the given context, or engaging in behavior that helps hide relevant information.
• Exaggeration: overstatement or stretching the truth to a degree.
• Understatement: minimization or downplaying aspects of the truth

Under this classification you can say that it is equivocation ('a car' is taken to mean 'some car other than mine' and 'my car' at the same time), concealment (the fact that this 'some car' is actually mine is hidden) and understatement (to refer to 'my car' as 'some car' is an understatement). Finally, even under this classification you can call it a lie ('a car' is made up, it is actually 'my car' and saying 'a car was stolen' or 'my car was stolen' is very different).

He's using a red herring!

Source: this web page says:

A Red Herring is a fallacy in which an irrelevant topic is presented in order to divert attention from the original issue. The basic idea is to "win" an argument by leading attention away from the argument and to another topic.

In your question, the original topic is about whether one of the characters (Me) caused a car accident. That person then starts talking something irrelevant -- observations that he/she has made about cars in the past, thus diverting attention from the real question.

A common tactic for telling the truth while intentionally misleading is by using the phrase: "What if I told you..." and variations of this. You can follow that sentence with a blatant lie and, due to technicalities, you can say anything without it being an actual lie.

Below is an example of a lie a history teacher once used to pass his interview:

Interviewer: You seem very personable and all but how much do you actually know about Canada's history? Tell me about John A. MacDonald.

Teacher: Well, I could tell you what your average Canadian knows about how John was Canada's first Prime Minister, how he secured the British North American Act, or how got his hands dirty in the Pacific Scandal and lost his office, but what if I told you that Mr. MacDonald was a rampant alcoholic who preferred his female companions to be between the ages of 11 and 13? What would you say then?

Interviewer: Well, Mr. McGregor, clearly you know even more than I do about our history.

McGregor referred to what he did as intentionally misguiding but he insisted that this was in no way a lie as he technically didn't say anything untruthful.

I think paradoxical diversion best describes what you're looking for.

I think the best way to describe your behaviour is to say you are being evasive. Google defines evasive as:

Tending to avoid commitment or self-revelation, esp. by responding only indirectly
‒ she was evasive about her phone number

This definition seems to aptly describe your situation.

It is also a behaviour seen commonly in politicians when asked a direct question!

There's the moral concept of a" lie by omission". For example, if asked "Did you eat the last cookie out of the jar?" and answer "No" because you palmed it and plan to eat it later, it's technically truthful, but a lie by omission of the detail that you did palm the last cookie even though you didn't yet eat it.

I have also heard the term "Elfish lie", coming from the tales of nature spirits who are unable to lie, but are masters at revealing facts in a misleading way.

You're leading someone to believe in something indirectly. This reminds me of politics. Demagogy may be the answer.

I must chime in with sophistry. Sophists can both tell the truth and deceive at the same time; and sophistry is a good word for the overall tendency.

Several directly-useful terms already have been suggested, such as derivatives of evade (in its “to avoid by dexterity, subterfuge, address, or ingenuity” sense), deceive (“To trick or mislead”), and mislead (“To lead astray, in a false direction”, “To deceive by telling lies or otherwise giving a false impression” or “To accidentally or intentionally confuse”). I will mention several more verbs that apply:

• tergiversate, “To evade, to equivocate using subterfuge; to obfuscate in a deliberate manner.”
• waffle, “To speak or write vaguely and evasively.”
• palter, “To talk insincerely; to prevaricate or equivocate in speech or actions.”
• diddle, in the sense “to cheat; to swindle” rather than a sense like to have sex with or to waste time.
• weasel, “To engage in clever or devious behavior.”

The following adjectives also are relevant:
• slippery, “Evasive; difficult to pin down.”
• cagey, “uncommunicative; unwilling or hesitant to give information.”

Sources: Wiktionary entries