It is much more difficult to get into med/law school coming out of a state university (or a no-name university) than a big name university. Sure, if you have a 2.00 GPA at Harvard or a 4.00 GPA at a state university, that may play into it. But I don't think it's true to just dismiss the power of how much help having a big name university on your resume can provide.
Here in California, I hope my kids don't go to Berkeley. It's been hammered by budget cuts, there are a zillion kids there, the labs/resources just aren't there. A private university, although expensive, maybe a better long-term investment for them.