I go to an Ivy that isn't on your list (Princeton), but I want to offer my advice.
Do not be deterred by what people feel is "weed out." The people who decide not to become a doctor are often those who find that they are not interested in science anymore. Hence, they do not study and do poorly on exams. They finish the introductory chemistry and never move on to orgo because they have no interest in continuing. Very few people at these top schools do not have the brain power to excel as a doctor. Becoming a doctor, however, requires a passion not only for the science, but also for the profession -- helping people through clinical care.
Do not be scared that you won't make it at a top school. Do not go to a state school just because you think you'll get all A's and you're afraid to fail. You will not fail if you work hard. I would always want to be in the best learning environment -- a place where everyone has a passion for learning and other passions beyond academics. This brings the best out of you. The experience of college is more than getting As. And if you work hard and are dedicated to doing well, you will get those As.
I can also attest to the importance of a prestigious name to getting into med schools. I know people try to think that it doesn't matter, but it definitely does make a difference. Of course, people from a variety of schools get into top med schools (or any med school for that matter). However, the prestige of the undergrad institution is also important. I have been fortunate to get into a few top 20 schools already, and I flubbed an MCAT section (7 verbal). I can assure you that I would not have gotten into one of these schools if I had not gotten As at Princeton. If it had only been As at my state school, I would not have been given this opportunity. At Princeton, my top grades are top against the brightest (for the most part) students in the nation. They all work hard and are smart. At a state school, however, some students work hard, but it is certainly not 100% of the class -- which is the case at Princeton (well, not 100% but close to it)
Therefore, do not choose a school based on a fear of failure. If you want to succeed, you will.
