The difference in quality of American medical schools seems to be negligible. Students from every medical school match into both competitive and non-competitive residencies, and perform similarly in test scores:

First, consider performance on the licensing exams. All universities, on average, have a 95% pass rate for their students. That also means that there is, on average, a 5% failure rate. Both Harvard and Drexel each have students perform at the top of the bell curve as well as those who fail outright. While there are differences in the average score, your performance on the test is based solely upon your own preparation, and not any magical instruction given by the school.

Knowing this, does it really matter where you graduated from?