I agree entirely with people who argue that it is NOT a random process. The whole "this is arbitrary" thing is something that entitled premeds like to think is the reason why every med school doesnt kiss their feet and beg them to join their class. There are no absolutes in a process that is handled by human beings, but each school is looking for something- we just don't know what it is. Some schools are better than others at sharing, whether officially or unofficially, what they look for, at the most basic level. That's why most people with zero research interest or experience wouldn't bother applying to Stanford, and people with extremely low stats don't bother applying to Wash U.
Not only that, but med schools don't have 150-person classes filled with the same exact type of person x 150. Usually there'll be one guy who's been published 18 times, one who's worked with the dead African babies, one who was a long-standing and very accomplished EMT, and yes, a couple whose grades and MCAT scores weren't perfect but whose life stories spoke to the adcom. I am glad this is the case, otherwise I'd probably go nuts being in a class full of LETs.
The way I think of it, while of course there are a few mishaps (some great candidates that would have been a really good fit for a particular school are rejected, while some are accepted who clearly don't belong there), med schools look for a cohesive group of people who could work well together and portray the school's mission and ideals. If I get rejected (this is especially true post-interview), it means that they don't think I'd be a good fit for the school- period. And you know what? Maybe they're right. They have much more experience than I do reading students' files and they have seen many classes before mine and know what works and what doesn't, who'd thrive and who wouldn't, and what kind of people would fit together nicely. If anything, I just figure they're saving me from 4 years of being in a school where I'm not really happy and in which I don't belong.