while speculation is nice from medical students who always seem to have strong opinions that are rarely grounded in factual knowledge, it seems like nobody really has the magic formula for success.
but maybe this will give some insight into the fact that going to a name place does matter to some degree (and i readily admit that the following is an example of the most extreme competitiveness and not a reflection of the vast majority of career options)....
i have personal knowledge of the residency director at one of the top five plastic surgery residencies in the country factoring in the "pedigree" of a student when he is rating his applicants. Granted, plastics is the most competive residency to obtain as there are only 77 spots in the entire country and each residency has no more than 3 spots. And this program is at the top of the field, but something to think about. And by the way, this guy actually cares where you went to college too, not just med school.
In some circles, people believe it is a general reflection of one's ability, drive, maybe even social status, that people do judge others by. It is a fact of life. And people don't take the time to determine whether or not you were able to get into harvard but decided against it for financial reasons. they just notice the name of the school on your resume and make judgements about you.
thats not to say great people and great successes don't come from the no name places. there are numerous stories of those successes, and often those people have their hearts and minds in the right places and are that exceptional as humans that it shines through such that they must be noticed, but lets not be naive either. where you train absolutely is a factor. not only for the name, but also because it puts you in touch with big researchers/clinicians who will write you a letter and you can network with in the fields of your choice. These same people will be able to have a positive impact on getting into your residency of choice. If you are at all thinking about academic careers or competitive specialties, it behooves you to think very hard about aiming as high as you can, with the knowledge that if you don't get into harvard (most people don't), it doesn't end your chances at anything, but it still would be better to go to harvard if you can.
Then again, most doctors in the world trained at their local in state med school, got excellent cheap training, are in primary care type fields and are treating the community in their surrounding area and are capable happy physicians who are respected in their community. Its a matter of the scale of what you want to do and where you want to be ten years down the road.
The process is self selective as well such that people who choose to pedigree themselves into scenarios that lend themselves to flourishing in a more local clinical practice do so by their own volition, while "gunners" (whatever that means) tend to pedigree themselves "higher" because they're bred that way or because they have a burning desire to achieve something competitive or academic. Thats why people sometimes find different "vibes" at differently oriented medical schools. Are you more comfortable around the students at Columbia or the students at State School U where all the students are from that state? Its not a better worse thing, its a choice for many talented students, and a fair share choose either option based on what is important to them. What is important to you?