This one happened - I was there (as an observer, not a principal). Only the names have been changed.

X was Professor A's first doctoral student, and their relations weren't good. Rumor had it that the first time A saw most of X's thesis was when X handed in the final draft.

By the rules, there had to be a non-mathematician on the thesis defense committee - let's call him Professor H. Professor H made a valiant effort to read the thesis, understandably didn't get very far, but decided he was going to ask a question at the defense, to justify his being there in the first place. So he says to X, I notice you didn't provide a proof of your Lemma 2.3.1 - how does it go? X says, well, 2.3.1 isn't my work, it's a well-known result of van der Corput.

This satisfies H, but A says, OK, it's a result of van der Corput - but, how do you prove it? Well, X was prepared to answer questions on his own work, but hadn't brushed up on all the previous work that his thesis rested on. He hummed and hawed, started to give a proof, got stuck - at which point A gave him a hint. Using the hint, X got a little farther, but got stuck again - so A gave him another hint. This went on for an excruciating fifteen minutes (which, I'm sure, felt like 15 years to X), until finally Professor N broke the tension by saying, say, just whose thesis defense is this anyway, X's or van der Corput's?