Alrighty folks, here is the deal. As a third year I will weigh in on the topic, as I am closer to the match and many of my friends have already/are now going through it in a variety of specialties. Elias514 has made some great arguments, but is only a first year and really doesn't know the criteria by which things are judged. For fairness sake, I'm a student at P&S and I turned down my very good state school to come here.
When interviewees come here, I tell them to look at the quality of the match lists at the school, because really one of the most important aspects of a medical school is where it's going to match you. Match lists are an indication of how residency directors view the quality of that medical school, because lets be real, you can't get a good idea of how good an applicant is over an interview day, only that they are not currently floridly psychotic. They are more banking on that student coming out of a certain school, which they think of highly or have had successful residents come from in the past. That is why P&S students match so well, because programs have had Columbia students in the past who were clinical superstars, and will take a shot with their younger collegues. While most medical schools have stellar applicants with great GPAs and MCAT scores, no all medical schools have great match lists, which is telling.
In looking at Yale's match list, referenced earlier in the post, I was extremely impressed. That is a match list that not many schools, if any, can top. Their graduates went to quality programs at quality hospitals. When I look at Michigan's match list, I am not as impressed. That is not to discount Elias514's arguments that UMICH has great programs and its students must be great to get into them, which to some extend is true; about 1/3 of P&S students stay at Columbia for residency, which is some part because the program is good and some parts because you get a home team advantage coming from that program's school. But, taken as whole, Michigan's match list is still not in the same league as Yale's or P&S's from the standpoint of quality programs specific to each residency specialty field. It's really not even close. Yale students match better in every specialty across the board, from internal medicine to ortho to peds to derm.
So, why would you choose the ivy league school over a state school? Because every door is open for you, and coming from michigan they may not be. Reverse how you are looking at the match list controversy and see where the residents at the top programs in the field you are considering went to medical school -- it is all ivies. If you are applying to the top programs that are the most competitive, you might not even have a shot coming from a state school no matter how qualified you are, because they will take students from more highly regarded medical schools. If you in the middle of the pack (or the bottom) at your state school, you are even more limited in your options, while at an ivy league school, every residency program is still within your grasp. I am by no means at the top of my class, but I still consider any program in the highly-competitive surgical subspecialty I am applying in to be a good shot for me; if I had the same record at a state school, I wouldn't even be matching and would have to consider a different career.
If you want to go be a community medicine doctor in private practice, a state school is probably a fine choice. But, if you want to work at CHOP, you better go to the ivy league school. If you want a competitive residency program, the ivy league school will give you a better opportunity to get in. Whether or not this is a fair way of doing it is still debateable. The residents that I have worked with at Columbia come from the best of the ivy league medical schools overall, and are superstars. The residents I have worked with at other hospitals have come from the state programs, and are not as good as the Columbia residents. Not proof, but take that as you will. Enjoy.