Most of the "best" universities are VERY selective on only admitting the best talent -- or the ones with a lot of coin. They are still tagged as the best universities.
A study in which I participated in on behalf of one of the nation's largest school districts showed how important that distinction can be. This district spanned a number of communities, ranging from affluent suburbs to poor urban areas. The difference in achievement, as measured by conventional means, was just as wide ranged.
Our study measured achievement differently, though. We looked at the best achievement measures we could find for the students when they entered the school and compared with the best achievement measures we could find when they left. In other words, we measured what happened to the students while they were in that school.
We found that NONE of the supposedly top performing schools were top performing by that measure. In every case, the students left that school looking pretty good, but in every case they had come into the school looking just great. They took platinum students and turned them into gold.
Many of the supposedly mediocre schools did the opposite, turning weak students into relatively strong students.
As for your other point...
It's commonly said around SB that, "it's not the agency, it's the instructor." I would say that it's not the instructor, it's the student. In this sense, the teacher doesn't teach, it is the student that learns. The teacher is just one more instrument of learning, just as experimentation, reference materials, research, etc. are also instruments of learning. Of course you have different degrees of quality among learning instruments, but the ultimate owner of the newly acquired education will be the student -- so the burden of actually taking effective and full ownership of such education consequently falls on the student.
In another study we did for that same district, we were able to identify really weak teachers in terms of what they were doing in relation to students and really strong teachers, and we surveyed them for a comparative study. (They did not know we were able to make that differentiation.) We found a 100% association between teacher attitude toward learning and their rates of success. The really poor teachers ALL believed that learning was almost exclusively determined by the motivation and native ability of the student--the teacher was just a learning tool the student used. Every single one of the top performing teachers believed that through effective use of instructional strategies, an effective teacher could make any student learn successfully.