What do you call someone who always talks a situation in their favor?
For example, Tom tells Mary that she has a piece of meat stuck in between her teeth. Mary replies "Oh I purposely left it there". How do you describe Mary's character?
The phenomenon you speak of has a distinct studied name which I remember from a psych class from long ago - ad hoc hypothesizing. If I remember correctly it is when you compensate for abnormalities or issues by creating false rationalization(s) about a topic - in basic terms, changing your reaction based on outcome. I would just call them a liar. These people are certainly pathological.
The thing about ad hoc hypothesis is that they are stated in a way that is almost impossible to prove wrong. In your example Mary states she purposely left the food in her teeth. It is almost impossible to discredit this.
Now if the person is just doing it on purpose to be funny they would be a smart-ass.
Also for a person who is kind of in-between the liar and smart-ass, the person who change an argument based on the end result would have circular logic. In your specific example this could work, but we know that 99% of people don't leave meat in their teeth on purpose.
Tendentious means, in the definition given by Oxford Dictionaries Online, ‘expressing or intending to promote a particular cause or point of view, especially a controversial one’. It is, however, normally reserved for weightier matters. You may therefore have to rely on something more basic, such as lying, in cases like this.
There is a phrase pathological liar (also known as Pseudologia fantastica, mythomania, compulsive lying) which means
a person who lies to the point of it being considered a disease or condition, an abnormally habitual liar
The term also suggests that the lying is without purpose or counterproductive, since it quickly becomes obvious that the person is lying.
There have been two repeated themes about this topic on the TV show Saturday Night Live. For several years John Lovitz played a character Tommy Flanagan, who nervously made up stories on the fly, eyes shifting as he winged it. He ended most of his lies with the phrase "Yeah! That's the ticket!" as he bought into his own lie.
Of more recent SNL vintage, Kristen Wiig has played Penelope, a woman who always one-ups her conversation mate by telling a whopper.