This became especially apparent during my first year of university where I took a macro economics course. Because I had already had a bit of calculus, so many of the mathematical problems in that course were almost trivial. Friends that didn't have any calculus found the course a lot more difficult because they had to memorize so many equations.
I have kids now and I watch them memorizing things and I can't help but think that's a waste of time. Remembering what the terms in the quadratic equation isn't nearly as important as remembering what the uses of the quadratic equation are. When do you deploy it? What does it give you? That's how I wish it was taught.
I think a good education is more about the student than the university. The reason for the strong correlation to the contrary is because good universities get to hand pick from those overachievers whom would achieve with or without said university. And that character development happens long before one's applying to universities.
That said a top university, its resources, and atmosphere of being surrounded by other top students, certainly helps foster even more success - but I expect if you take the average merit admitted MIT student and transplanted them into Party State U after 4 years you'd still find an extremely 'well educated' individual. By contrast, transplant your average Party State U student into MIT and you'd find a dropout.
Source?