I would say, to firm that up even more, every school can point to their accomplishments, and the graduates/professors that worked on them, as to why they are in rarified air. You can look through Wikipedia at all of these renowned scientists, and who their advisors were, and who their students were. So you can say they stood on the shoulders of giants, and also stood tall for others to perch even higher.

But not a single one of those heroes of science should rightly be remembered primarily or even secondarily because of where they studied.

The underlying fallacy is that you can only learn the best skills from the best people in a short window if time in your early adulthood.

I'm not sure I understand how this is relevant.