Several years ago I helped a strong applicant who had been rejected by a top medical school. He thought he was a very good fit for this particular institution, so he called the school to make his case. Surprisingly, after the applicant's phone call, the school granted him an interview, reversing their original rejection.
It was at this time when I met the applicant; we conducted a mock interview so he would be well-prepared.
Ultimately, after being initially rejected, this applicant was admitted to that top school.
Of course, this is an exceedingly rare occurrence. But to me, the moral of this story is that it is worth being assertive (not aggressive!) in the medical school and residency admissions processes: Send an update letter, call institutions (politely) to inquire about your status (if they do not expressly prohibit phone calls), and be proactive during your interviews.
You need to advocate for yourself in order to be noticed.