(OP): To be more clear, it's not FizzBuzz per se but the general idea. In reality it's always more complex than the original FizzBuzz problem (I've never actually seen something that simple.) It usually goes "solve this puzzle". "OK, now can you do it faster?" "I see you have a syntax error, what is it?" (Two minutes later, oh crap I forgot a semi-colon.) And then repeat all of that with three other people, each with their own puzzle.
It's easy, for me at least, to freeze up at any time in that process and stop being able to do anything at all, even if in a normal work setting it wouldn't be a problem. It seems rather ridiculous, or at least frustrating, that the job hinges on that process.