Most of the concepts I learned, although I don't remember learning Kadane's algorithm for solving the maximum subarray problem in school, so I've learned some things like that. I can also implement a solution for an associated Leetcode problem in one line of code, so I wound up memorizing that too.
OP says "If you master the methods and ideas, you should be able to derive the answers on the spot", but I hear from a lot of people that does not happen, even (implicitly) in this thread. Any how, even if I use OPs method, if I do the same problem over and over and over again I'm going to wind up memorizing it any how.
Some people are closer to each other, and upon realizing that they believe they've found a pattern. But it's like when people tell you that you need to supplement x in your diet. It's possible that x helped you. And it's even possible that you'll find other people with the same nutritional deficit, creating the illusion that everyone would benefit from supplementing. But that's just what it is: a premature extrapolation from anecdotes
Just for the record, that never actually happened. It's just a thing the homebrew guy made up.
(I know, the rest of your points are unaffected by this. I just feel annoyed when we casually warm up old myths.)
I tried to find some outside sources, but nothing about Howell admitting his 'artistic license' outright. So take my fallible memory with a large pinch of salt.
See https://news.ycombinator.com/item?id=15713801 for some discussion, and to see how 'invert a binary tree' wasn't even an established term that anyone at Google would have used.