What I think end up happening with those Fermi Problems (or other problems) is that the interviewer knows one specific answer and then ends up rejecting alternative answers
I know Google has interviewers copy down character-for-character what is written on the whiteboard for their whiteboard programming questions. Presumably this is so that their hiring committees can dispassionately review what the candidate produced, instead of relying on the interviewer to report success or failure.
Which is the reason they could be completely different from brainteasers, but are the same in the form used in interviews. People are very, very bad at evaluating on the spot if some "solution with thought-process" which differs from their own is actually completely valid, usually it is: "Nope, that's not how you do it. What did he think?!"
You'd have to capture the answer and then study it later, possibly multiple times to overcome any: "Hm, this doesn't sound right, why didn't he think of x, y and z"-feeling and understand that x, y and z are just your bias, not some kind of "correct" part of every answer. I've never seen that happening.
What I think end up happening with those Fermi Problems (or other problems) is that the interviewer knows one specific answer and then ends up rejecting alternative answers