I agree with your analysis. However I've only ever sat in on a few programmer interviews, and was lucky enough to get only the few that had already made it through several screens and were quite sharp. However, if so many people can't do FizzBuzz, that's baffling. If they can't do that, what can they do? I mean that literally. Do they just have knowledge of certain specific frameworks or something? Can anyone shed light on this?
I know this may be derailing the conversation, and it bothers people, I'll not mind deleting this post.