I see what you mean, but in my experience there's this tendency where you think you're testing for "X", but you aren't really.
A whiteboard FizzBuzz might be actually testing for memorization, deliberate interview prep, extrovert tendencies, etc. And not for any kind of actual technical skill. Failing the FizzBuzz could also just mean high social anxiety.
Or don't even try and make X not even intersect with anything you need.
It still puzzles me how many people opt "don't even try".