I really do feel like the undergrad you attend is significantly weighed in the MS process. I went to some backwoods SUNY that is best known for its Education/Music programs.
I forgot to mention this in my post; this is quite true in my experience as well, more at some schools than others. My fiance and I both went to a well-respected public college, but nothing fancy. She had very high numbers (I think it was 3.95/3.95/40 MCAT, which is 99.8 percentile) and good extras (lots of volunteering and experience in medicine, as both her parents were doctors) and didn't even get interviews from a lot of the Ivy league schools - Yale, Columbia, Harvard - though she did at Duke, Chicago, and some other biggies. Her friend who went to a very prestigious private college had lower numbers and fewer extras, but snagged interviews at Yale and Harvard.
Some of the schools are much more numbers focused than others. Part of the reason there is there is really no iron law of USNews rankings where you absolutely must take the top scores/GPA's you can get. It's not the med schools aren't ranked, it's that (1) those rankings are a lot less consequential for the lives of most of the graduates and (2) the rankings mostly wind up being based on prestige and the research produced by the schools, not by the incoming MCAT scores of the students. Research bears almost nothing on the lives of the majority of students who have no interest in medical research; what matters to students is the ability of the school to place students in the specialties they want (although there are of course students who don't want to be specialists). This ability is somewhat correlated with the prestige of the school, and indeed the really competitive specialties usually require involvement in research beforehand, which is easier to get at major research schools. But there are plenty of schools that are not fancy research schools that place a very high percentage of students into desirable specialties, so regardless of prestige those schools are very good options for the students.
The undergrad prestige thing, honestly, is part of the wider fact that med school admissions (I mean top med school admissions, not regular public school med admissions) are a lot tougher for students of lower income backgrounds than are law school admissions. Anyone can get good grades, and it doesn't matter where. The LSAT can be learned by getting like 30 practice tests for $50. Do both of those and bam, you've got at least everywhere outside Yale and probably Stanford.
Med school, though, basically sets before you a bunch of tasks that are possible for anyone but way, way easier if you come from an upper middle class background. Shadowing opportunities? Much easier if you have relatives who are doctors. All the forced volunteering? Much easier if you don't have to work concurrently. MCAT? My fiance was scoring high 20s before a $2000 Kaplan course. And of course there's the prestigious undergrad, and socioeconomic diversity is not a serious goal of most top UG's. (I think the Crimson said last year that financial aid records suggested about 70% of Harvard UG's came from families in the top 10-20% income wise. Some, like Dartmouth, take this stuff more seriously.) Oh, and there's the fact that applying to med school - if you're applying to the prestigious top med schools - costs literally thousands of dollars. You wind up attending interviews on two or three week notice, paying thousands of dollars for last-minute plane tickets, hotels, cabs, application fees, etc.
Of course the flip side of all this is, as I said, unless you want to be a researcher or just hunger for DAT PREFTIGE, prestige of medical schools is not terribly important to the students attending them.