There are two ways of “doing fizzbuzz” or any other small interview programming problem

1) in an editor, iteratively, until it works. This is the correct way. Every developer should manage to solve FizzBuzz in this setting.

2) By writing it on paper or a whiteboard without feedback. Even the greatest developer in the world would randomly fail this. It provides zero information about the capability of a developer and no one should ever subject anyone to that type of test.

meh. Fizzbuzz is short, and you should be able to read simple code and predict its output. If you botch, catch the error, and fix it, it's a good sign. If you can't find the mistake in five lines of your own code (say, because of overconfidence...) then it's a bad sign.

(I would argue that 'now, find a bug' is a good follow up question in most any coding interview, regardless of how perfect the first draft was...)