agreed.
check out the backgrounds of the chiefs of services at many of the nation premiere hospitals, and you'll see an amazing variety of backgrounds: truly a real variety.
if you go to a "prestigious school" and you train yourself well, you'll be a tremendous asset to your patients and your profession.
if you go to a "not-so-prestigious school" and you've got the right stuff, you'll be able to hold your own anyday, and people WILL recognize that and will tap into your talent.
the point being, build up your skills: really learn to think and reason things out, be a skilled communicator, learn to listen, work well with your team, have grace under pressure, get real world experience and you'll do very well, whatever your goals are, wherever you're from.
best,