This! This is the thing that most people forget.
If you are capable of getting into Berkeley, or Cal Tech, or MIT, or Cornell, you’re probably the kind of student who will on the whole be ultimately JUST as successful as a student that chooses to go to Rutgers or Binghamton or UNCC. In fact, I’ve personally seen that studently in the top 5% of one of those less prestigious programs get the plum research gigs with the best profs, the best internships, and the best opportunities post-grad, because it’s based on the drive of the student.