This debate has been going on for years and only the adcom at the universities really know the answer. One thing I have noticed working a top academic hospital/university for years is that the doctors who receive fellowships at our program, we have six every year, have always come from top ten universities. Be it, Stanford, Harvard, Yale, Duke, Washington St. Louis...etc. That being said, it may not take a person from a great undergraduate program to get dental school, but the ones who have excelled the best at the graduate level seem to come mostly from top notch schools. This maybe because they have had more experience with cut throat competition or whatever, I dont exactly know. Of course there are exceptions, but I've rarely seen them at our institution.
Personally, I do believe a person who went to a top rated school should be awarded brownie points when compared to a person who went to "UoH". But that person who went to the top rated school better show they can do well on the standardized test, otherwise they lose their credibility. I don't buy the whole argument about people who are geniouses who dont do well on standardized tests. That may fly for high school SAT's when no one knew what the heck a standardized test was and how to study for it. But if you have graduated or come close to graduating from a 4 yr institution, you better know how to study for any test that comes your way by now.
The only test I know of that has some sort of inequity in it would be the MCAT's since it is heavily based on passages. A person who learned English as a second language may find it unfair. For us DAT takers, I dont find that bias. And no, I've never considered taking the MCAT's, this is just a complaint I have heard from people who have taken it.