I applied for an MSTP at a UC and wasn't offered an interview for it, but was for the MD program. I appealed for an interview for the MSTP and got one. (Still waiting to hear back on the outcome.)
My stats were easily in range and I had an excellent letter from a clinical faculty member at that UC that I had worked with full time for over a year, and I had a "significant other" enrolled there. I used the letter to talk about how well I knew the culture of the school from working there, and why I thought it was a good fit.
The MSTP admissions folks that I talked to about it were totally happy to accept the appeal, and didn't seem put out at all. The attitude they had was something like, "We make mistakes sometimes; we're happy to give you another look if you give us a good reason." I suspect that the MD post-secondary appeals are handled a similar way.
-CHO