The thing the fame of your school that affects the most (IMHO) is the importance of class rank. At a big time school, a high class rank is going to help you more and a low class rank is going to hurt you less than someone coming from a "lower tier" school. If you're top of your class at John Hopkins, that'll turn heads, but if you're around the middle they'll give you some leeway since it's such a known school and probably has a stellar class. If you're from a school no one's heard of, they're going to give you less credit for top of the class and if your class rank isn't that great that might hurt you.
But everyone is right in saying individual effort is paramount here. If you wind up in the lowest ranked medical school in the nation and wind up with a top class rank, an insane board score, and letters of recommendation that make you look like an all-star, no one's going to care where you came from.