I would lean towards The Knife & Gun Club's opinion.
Of course, there's a self-selection process going on in that the best med candidates come from top undergrads, so they're likely to get accepted to top programs if they desire, but I have a hunch that it is disproportionally so. Lots of incest and nepotism. At least for MD/PhD interviews, I was always on the lookout for current students and applicants from state schools or low-tiered schools. I did not meet a single applicant in all my time who came from FL, or even a southern school (non-Duke, etc.) for that matter. As for current students, those that did graduate from a low-tier/state school did multiple gap years as research assistants at places like MIT, Hopkins, NIH. In fact, at WashU MSTP, only one person in the last decade has matriculated from my alma mater (only last year and he did a gap year at Hopkins). In a whole decade. I don't think anyone in the history of Hopkins MD/PhD. At Penn, I met one girl from FAU, but she did research at MIT for a couple of years. Of course all these people worked extremely hard, and given the large population of state schools (mine has 30k undergrads and ~760 med school applications each year), I don't think there's any shortage of qualified applications that warrants one person per decade, or only a handful each cycle that matriculate to T10 programs - MD or MD/PhD. Of course there's going to be people like me or Rainbow Zebra who have absolutely no affiliation with a highly regarded name brand who also get into a highly regarded med school, but on a population basis, I am sure it's not common.
So in my absolute humble opinion, name brand can mean a lot - if you want to go to another name brand institution. I don't agree that there's only a small value. The weight is pretty large.
At least for IIs, I've met candidates at interviews where I've gotten into very open discussions about ECs, stats, publications, etc. who also go to Hopkins or other similarly regarded undergrads, and I'm just like how are you here with your record (didn't say that, and absolutely not to be rude). They had awkward/off-putting personalities (in that I woulnd't want them to be my mother's doctor or give me a prostate exam) and can't imagine they may have had some back story up their sleeve. Maybe they did. Of course, this part is anecdotal from my application experience, but I worked my butt off to even get an II at these unbelievable programs - so this explains why I may think this way.
Again, this is just my experience/bias. And I know some coming from similar backgrounds have had the same experience.
I'm still trying to wrap my head around all this - the nepotism and incest at these institutions. How palpable is it, truly? We'd of course have to normalize for the self-selection bias.
