People are not generally answering interview questions based on instinct, but rather based on what they think the interviewer wants to hear to get the job. I would have interpreted this is as a leetcode style algo question and started by treating it as such, even though IRL my first instinct would be "get a lib that does it". Awful, awful strategy.
It appears that either answer would be accepted, and so I'm fine with it. If it really is there is one correct answer then I'm against this. This feels like a problem where a good enough solution can be done in the time of an interview if you do it by hand (though if anyone knows about dates they will expect there is a lifetime of fixing special cases left if you don't use the library)
I prefer fizz-buzz as a question because it is obvious there isn't a library. It is also a problem you should be able to do in an interview. It has enough weirdness that there is no best answer, despite having several workable paths you could try.
Nope, not remotely awful. I've made great hires from it, which is its point.