I think people are anti-prestige here for good reasons... Particularly when you have choices between schools with basically undeniably equal opportunities. At that point, "prestige" can cloud judgement in swaying a candidate to pick a school they may be less happy at (for geographical, cost, 'fit' or "people" issues) or regret choosing down the road when they realize that the added prestige really didn't affect much besides their bragging rights. If this really is that important to you (to know you go to a prestigious institution), I understand and acknowledge that should be a part of your decision making process. Everyone does have different things that make them happy.
I think the relative prestige of your medical school (to a small extent) can affect perceptions during residency applications. But, just as in undergrad, students who attend prestigious medical institutions attend prestigious residency programs probably less because of the influence of their own institution and more so because of their personal motivation and drive. Top institutions see a higher number of students at top programs because they have already selected a small group of highly motivated individuals. These students would have achieved the same results at any other less prestigious institution, given the institutions offered similar opportunities (research, travel abroad, etc.).
I'm sure you can argue that point, but from my personal experience...I've met a fair amount residents/fellows at the #1 pediatric institution in America (where I work). Some attended medical school at Harvard, some attended NYMC. I honestly couldn't tell the difference. They were all motivated, smart people and got here because of that.