The problem, from my perspective, is you think this is something that needs to be 'known', rather than a basic skill. I think it is basic.

I don't want somebody who 'knows' how to invert a tree, any more than I want someone who's learned the answer to Fizzbuzz.

The point is not that you know how to do it, but that you can naturally perform basic manipulation of very simple data structures. If you can't swap two values, or you can't write recursive code, you may think you're a competent programmer, but I don't agree. What is basic, if that kind of thing is advanced?

If you think an employer expecting that level of competence has 'a sort of attitude', then I don't know what to say. How would you react to someone who felt that way when asked if they could code a loop over a pair of lists, or return a function from a function, or any thing else you consider routine (do you consider anything routine)?

It worries me that programming has become 'copying and pasting from Google' and that people would find it offensive that anyone could possibly have a higher standard than that. If that's a horribly elitist, unacceptably arrogant attitude to you, then again, I don't know what to say.