As someone who has studied at both kinds of schools I can tell you there is a WORLD of difference.
In a middling school the professor was constantly providing remedial education to the students and had to cut down the curriculum breadth and depth.
When we are talking about the elite 0.01% of students the professor is irrelevant for regular coursework. They are almost uniformly autodidacts. A mentor is of course useful at the very boundaries of knowledge that textbooks and papers don't cover. But by the time you are in that range of work, you will be recognized through your performance, and you can find mentors by reaching out to them with links to your work.
Generally, people are completely unaware of what top 0.01% of performance looks like because we are so rarely around these people unless we are in some very elite institution or working on some project which attracts such people.
