I talk to people about interview stuff, I notice that most people who say "I shouldn't have to know X" seem to be the least intellectually curious, least great problem solvers and just generally combative folks. If you are going into an interview with a serious chip on your shoulder, demanding a job, asking to exempt yourself from having to show problem solving skills, then just how is that going to work out?

Regarding reversing a binary tree, yeah, the interviewer didn't expect you to know it. That's the point. It's something that's a little tricky, not impossible, requires you to be precise about memory ownership and pointers, and algorithmic. It takes no time at all to describe, and isn't impossible to solve. Yeah it's problem solving, but it's not random trivia. It's a functional test of your intelligence and yeah it filters out some who should be at Google, and they know it. However relaxing the bar is fraught with peril. You're quite literally banking the future of the company on it.