I was good at math growing up but not in a "#1 in the world" way. I've been to a couple of math contest national finals. So I naturally have seen many "geniuses". Some of them when they see a problem sometimes just come up with the answer immediately. These are questions that require procedural thinking so I couldn't understand how it was possible to come up with the correct answer instantly. One day I asked him. He said he doesn't know but sometimes he can just "see" the answer. I used to think that's bullshit, but after having experienced more of life I think it is not entirely impossible.

We have no idea how brain works, so we can only make hypotheses based on experience. When someone can "see" an answer without being able to explain how he came up with that answer, regardless of how useful that skill is in the real world, that is something. Maybe sometimes all his neurons connect instantly in certain circumstances. Who knows.

Another reason I think this is possible is because sometimes I come off that way (to much lesser degree) to other people. Sometimes when I come up with a solution to a problem (not at all domain specific), people wonder how I can do that. I can't explain of course. I am not trying to say I'm a genius. I'm saying things like this happen sometimes for no reason. And "highly intelligent" people tend to have more of these than "normal" people.

Anyway, these are all just theories, yours included. So I think just saying that our brains objectively work in certain ways is not a good idea, and is probably wrong.