Adding to the list:
Harvard
Columbia
Emory
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Forget about academic excellence, they want outstanding *individuals*, people with a demonstrated potential in research and with leadership qualities. (They are NOT interested in financing students who most likely end up in private practice in the long run). MCAT > 39, GPA > 3.9 and a career in volunteering help only to secure secondaries. Seriously. Lots of folks have those, that doesn't get admissions excited about you and keen on throwing money your way.
Most people need fin aid for med school, and fin aid is available for just about everybody. That's why scholarships tend to be merit based.