At many schools, it is *possible* to get a great education, but you have to actively seek it out - it isn't mandatory. I got a much better education than many of the students I went to college with because I took the time and effort to meet with my professors regularly, read all of the additional suggested texts (and asked for more), and actively engaged with the material, instead of doing the minimum required. The questions that I was asked on my exams didn't really make me think, but the ones that I asked myself outside of class did, and I made sure that I took the time to explore those questions in depth with anyone who would let me.
I didn't attend a big-name school, but I did end up well-respected in my field, and so did many of the students at my school who took the same attitude toward their studies that I did.
Would more doors have opened for me and would I have made social connections that would have been helpful if I had attended a more highly ranked school? Probably. But I really do think that determination, skills, perseverance, and passion probably matter just as much, and those are not dependent on the whims of admissions committees.
In my experience, many gifted individuals are perfectly capable of being autodidacts, given access to a university-level library system and contact with even a few mentors willing and able to discuss areas of interest.
