Someone who can't do it is definitely not qualified to do fizzbuzz level programming off the cuff in a stressful interview situation.
Whether that tells you anything about their ability to do fizzbuzz level programming in a more normal work environment is an open question.
There are a few HN readers who've had experience of "choking" on fizzbuzz level programming tests during interviews - even though it's trivial there's something about the interview situation that causes some people to sometimes freeze.
