Who cares if you can invert a binary tree? Who cares if you can write a binary tree? I know what I've needed to know really well, because when it hit me in the face, I learned it. If I need a self-balancing whatever, chances are I'm gonna grab one off the shelf and call SomeBTree.new(args).
The problem with "maybe you should have just learned those simple concepts" is that there are an infinite number of clever questions interviewers try to ask, and close to none of those questions matter. The management that wants to have confidence that applicants can verse a binary tree is also the management that would not let you budget the time to create a binary tree if you actually needed one from scratch... "you shouldn't have to worry about that, just ship it and move on".
Most of my job as a dev seems to be cleaning up the messes of someone that cleverly coded everyone else into a slow, unmaintainable mess. How interviewing for that?!