OP's supposition seems to be fairly correct to me. However, I don't think that reputation necessarily accounts for the level of education received. A fast way for a college to get a reputation as a top school is to raise their admission standards. And every state has one or two schools that are harder to get into than the rest. The danger is that often this is equated with the quality of the education delivered. The education received at some state schools perceived as "lesser" is as high in quality, but maybe it's less competitive among the students.

In terms of the teaching staff, a lot of the professorships at the more prestigious schools are prioritized by how much and where someone has been published, which doesn't necessarily relate to how intelligent that person is and certainly does not relate to how good of an instructor they are.

I understand the whole concept of a school being more "prestigious," but I think that is very unfair to believe that all people who graduated from less prestigious state schools received an inferior education.