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I think, it's not an assumption, but a fear that this is the case.

Adds some extra anxiety as interviewee still worries about their code being correct or not. No one wants to risk being frowned upon just because they've messed up some syntax fine point. And since people are different, sometimes it really happens.

This can be avoided if interviewee's specifically told they just have to write algorithms in pseudocode, but it's not how it always goes in practice.

Because sometimes you are expected to write working code on whiteboard. Once interviewer was typing code I wrote on laptop and interrupting me on errors he had.

Exactly! When I was hiring I was even asking question I did not know answers to (not as a canditate, but as an interviewer).