I believe the term colleges use for this is "demonstrated interest". Take the following scenario: Say Sally applies to two non-"top tier" medical schools, as well as top-ranked Herpvard and Derpkins, with stellar stats and ECs.
Herpvard and Derpkins, knowing their reputations precede them, assume that Sally would bend over backward to attend their medical schools if she were accepted. So they interview her and see what happens.
University of Herp, the flagship university of Sally's home state, also sees Sally's strong application. They also see that one of her parents attended U of Herp, and that both her folks live in the area. Sally even took a couple of classes there over the summer. So it only makes sense that they give Sally, an above-average applicant, an interview.
Derp State, however, is three states over from Sally's home state of Herp. They see Sally's stats, which are impressive; it's only natural that an applicant of her caliber would also apply to Herpvard and Derpkins, as well as at least one school in her home state. But they also see that Sally has taken summer classes at U of Herp, that she has family ties to the area and the school, and can find few reasons why Sally would apply to Derp State at all. They could ask her to fly in for an interview, take the time to see what she's about--or they could use that same time slot and those resources to interview Harry, who is from just two hours away from Derp State and has similar stats. It's not that they wouldn't love to have Sally--she seems like a great candidate; but Derp State sees so many more applicants who have ties to the area, and who would be more likely to matriculate AND thrive there. So they wish Sally the best, but decline to interview her.
Sally wasn't rejected because her scores were TOO HIGH, but because Derp State has limited time and resources, and because Sally may not have been as enthusiastic about attending Derp State as many of their other applicants--which means that there is both a low chance of her accepting an admission offer, as well as (perhaps) a higher chance of her being unhappy (and potentially less successful) at that medical school. And yeah, maybe they'd like to protect their yield numbers a little bit, too--though one applicant won't sway those numbers too much either way.
My point is this: Yes, medical schools take a risk with each applicant they interview, and each one they admit. There is a certain amount of gambling that goes into it--or perhaps a better way to say it would be to call it a cost-benefit analysis. It's a slightly more complex process than "oh, they just threw me out because my stats were sooooo high" or "you didn't fit their mission statement", you know? Medical schools take pride in their students and hope their students take pride in the school, and part of that equation in the admissions process is demonstrated interest; no school is going to throw away an admission offer or an interview slot on someone whom they believe has little interest in the school, be their stats high or average or low or anywhere in between.
Herpvard and Derpkins, knowing their reputations precede them, assume that Sally would bend over backward to attend their medical schools if she were accepted. So they interview her and see what happens.
University of Herp, the flagship university of Sally's home state, also sees Sally's strong application. They also see that one of her parents attended U of Herp, and that both her folks live in the area. Sally even took a couple of classes there over the summer. So it only makes sense that they give Sally, an above-average applicant, an interview.
Derp State, however, is three states over from Sally's home state of Herp. They see Sally's stats, which are impressive; it's only natural that an applicant of her caliber would also apply to Herpvard and Derpkins, as well as at least one school in her home state. But they also see that Sally has taken summer classes at U of Herp, that she has family ties to the area and the school, and can find few reasons why Sally would apply to Derp State at all. They could ask her to fly in for an interview, take the time to see what she's about--or they could use that same time slot and those resources to interview Harry, who is from just two hours away from Derp State and has similar stats. It's not that they wouldn't love to have Sally--she seems like a great candidate; but Derp State sees so many more applicants who have ties to the area, and who would be more likely to matriculate AND thrive there. So they wish Sally the best, but decline to interview her.
Sally wasn't rejected because her scores were TOO HIGH, but because Derp State has limited time and resources, and because Sally may not have been as enthusiastic about attending Derp State as many of their other applicants--which means that there is both a low chance of her accepting an admission offer, as well as (perhaps) a higher chance of her being unhappy (and potentially less successful) at that medical school. And yeah, maybe they'd like to protect their yield numbers a little bit, too--though one applicant won't sway those numbers too much either way.
My point is this: Yes, medical schools take a risk with each applicant they interview, and each one they admit. There is a certain amount of gambling that goes into it--or perhaps a better way to say it would be to call it a cost-benefit analysis. It's a slightly more complex process than "oh, they just threw me out because my stats were sooooo high" or "you didn't fit their mission statement", you know? Medical schools take pride in their students and hope their students take pride in the school, and part of that equation in the admissions process is demonstrated interest; no school is going to throw away an admission offer or an interview slot on someone whom they believe has little interest in the school, be their stats high or average or low or anywhere in between.