I really don't think I am making that claim. As far as I've read SAT scores before the age of 10 are a good marker of intelligence. Of course you can prep a large extent to get into a good school as a high school student.
I attended a small state school for undergrad, and a top school for grad school. There were no extraordinary students at the small state school. I was top of the class. When I went to grad school I was quickly humbled as very much average in that selected group. Everyone studied/research all day long in grad school, it wasn't really a matter of who was more driven, everyone was driven.
All my point is and has been, is that extraordinary people self select to go to good schools. That brings up the average overall compared to low rank state schools.