We had visiting researchers from anywhere and I failed to see any correlation between the two things in years.
I can tell you none of the brightest came from cambridge uk or harvard us but universities you never heard of in southern italy or india.
Your entire argument that follows is delusional.
Nothing about going to Harvard makes you more qualified in maths, e.g. than going to any European public university you have not heard of. Education depends on the quality of teaching and learning, and most great professors in important universities excel at funding, not teaching.
Even when it comes to learning, especially in stem, you will likely learn more on books and internet and your course mates than your lectures. Hell, internet is filled with all the lectures you want from Harvard, MIT and more elite universities. As for any university in the world there are good and bad courses.