Learn English – Term for the identification of the person speaking in a dialogue

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.

When dealing with anyone you do not know extremely well, it is never wrong to be correct.

Being correct means you will respond to any query about your well-being. And, you will reciprocate.

Good morning, Jim, are are you?

Quite well, thank you, Bob. And you?

is good short form of correctness.

Greetings should never include anything negative, except in very unusual circumstances. If you cannot bring yourself to say "Quite well, thank you", you can smile and say:

Better than I deserve, thank you

Again, it will never be wrong to be correct. No matter what some others may seem to be doing, be correct. You will, on balance, make a better impression on people if you are.