I've never been asked to "invert a binary tree" while interviewing at Google, or anything of the sort; later, as an interviewer myself, these kind of questions were forbidden. Everyone knows they're stupid, and they've been forbidden for a long time. I'm starting to believe this is either a persistent myth, or something the other companies, but not Google, does.

In my experience, all the questions I was asked were fair game - all of them were about implementing a toy version of a real-life feature (simplified for the time constraints of the interview). All of them felt like "yeah, a competent engineer should be able to do this".