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.
Do you have any evidence to prove this? I've never seen any research that supports what you are saying. And, I've see quite a bit of anecdotal evidence of state u or less well know college grads doing very well in admissions.
I have not, either. Regarding law school, a recent NYT article
http://www.nytimes.com/2011/05/01/business/law-school-grants.htmlLaw Students Lose the Grant Game as Schools Win
mentions that law schools offer scholarhips to improve their selectivity, which is based student GPA and LSAT scores. I did not see any adjustment of GPA for prestige of undergraduate college, and given the grade inflation at the Ivies, doing so might be double counting. I think an aspiring lawyer can get into law school from a public university, as long as he/she has good grades and a high LSAT. I'm not a lawyer, so this is conjecture.