I do not object to the broad points being made here but I do object to this interpretation. It's beyond awkward for many good valuable programmers, stifling really, to do this kind of unrealistic audition programming for a live audience. You are not just under stress -- you are far, far, far outside of any demonstration of your true value to the employer.

Perhaps the hiring pool really is that bad, you have a giant pile of unqualified applicants, and you really must use this kind of blunt instrument rather than taking the time to talk with candidates and their references and really get to know their work and their reputations. I've never had to do hiring and I don't envy you if you do. But I've also never in my life had to do this kind of test, and I think I'd use it as a filter myself to avoid working for someone who uses it.

[EDIT: I assumed it would be clear that I'm not talking about the coding challenge of FizzBuzz. I'm talking about the experience of audition-style programming. You end up filtering on less important characteristics of applicants who might otherwise be your best candidates, but think you're filtering on FizzBuzz.]