That said, for FizzBuzz proper, one should have dozens of solutions memorized for these situations, but for similarly easy questions the candidate might not have come across that might end up being a big deal.
I've definitely felt that pressure as an interviewee. It's pretty disheartening to write a simple and obviously correct implementation only to have the interviewer express their disappointment that you didn't use a particular optimization.
The most fun technical questions I've had start with making a functional algorithm and then massaging it to meet whatever time/space complexity requirements are asked for. Sometimes it results in a complete rewrite and that's ok, the real world works like that too.
I almost always preface whiteboard coding sessions with "I'm going to write some dumb, slow code and then we can make it faster if you want. Sound OK?" I've never had anyone disagree with this, but if they tell you they want you to go straight to the clever solution, hey, now you know what they're looking for.
50% of working programmers can't write a for loop? Does that square with your experience outside of interviewing?
I don't quite buy the whole fizz-buzz story, though I don't have an adequate explanation for what could cause these kinds of failure rates. Something seems very off.
Not 50% of working programmers, but of the programmer applicant pool. The applicants who can find jobs quickly aren't in the pool very long, and so it's dominated by the fakers and those who otherwise shouldn't be there. ... Which should make the reported phenomenon a little more believable.
And you know what? More than 1/2 the people that claim to be doing a job writing code right now can not do it. If you can't write a simple loop in your preferred language, I have to wonder how you are doing coding right now and being successful.