How do you figure from a Fibonacci exercise that the candidate understands recursion? It's 5 lines of code to memorize.
Second level is how they explain the simple recursion that’ll hit stack limits (i.e. without tail recursion)
Third level is using accumulator/tail recursion.
See how they can express these ideas and are they able to effectively communicate their intentions.
I'd still have you write the full thing out, but I'm guessing you'd do just fine.
Only when the interviewer finds someone “smarter” than himself does he approve of hiring the candidate.
It is an ego game.
Perhaps this describes OP.