I cannot recall the last time I interviewed someone for a position other than intern who could not at least muddle through a FizzBuzz problem. I'm talking hundreds of candidates. The likelihood of a "lucky streak" as long as that if "can't FizzBuzz" is common (i.e. not an outlier) is small.
Usually when I dig into a person claiming "can't FizzBuzz is common" the result is I find what they're calling "FizzBuzz" is nothing of the sort, but is actually a more tricky data structures or algorithms problem.