> Is it not possible that among them, you might have missed other candidates whose broader set of experiences would have taught you something that you didn't kn

> Is it not possible that among them, you might have missed other candidates whose broader set of experiences would have taught you something that you didn't know, something more important than the fact they failed FizzBuzz, for whatever inconsequential reasons? Sure, it's possible, but that's the best case scenario. What makes you think it's more probable than the alternative? Hiring someone who cannot program for a programmer role seems to have many potential drawbacks, have you considered them? When your money is on the line, you either learn to make decisions based on probabilities and expected values rather than mere possibilities, or you lose your money with high probability.