Do Colleges Ever Reject Overqualified Applicants?

This may be a ridiculous question, but I'm wondering whether colleges ever reject students whose test scores and GPA are well above their average range? For example, if someone with a 2400 applied to a school where the average SAT score of accepted students was a 1700, could they get rejected? My thinking is that some middle-of-the-road colleges might see an extremely high-achieving student and think "oh, there's no way this person is going here" and reject them to avoid using up a spot that could be given to a more likely prospect.

There is some controversy about this. It does appear to happen at some colleges, but not just because an applicant is "overqualified". Colleges that are traditional safeties for students who are really hoping to get into more competitive top-tier schools sometimes reject or waitlist candidates that they believe are not serious about attending.

Admitting too many students who clearly have no intention of actually enrolling will bring down the college's "yield" (the percentage of students who attend out of the number of students who were admitted). This can make them look less attractive to future applicants. Some schools specifically ask where else you plan on applying so that they can judge the odds of you attending after being accepted.

However, this phenomenon isn't based on a calculating group of admissions officers who have just decided to deny the strongest applicants because they don't trust them. The more salient issue is that many "overqualified" students will dash off applications to their safety schools. They're sure they'll be admitted based on their scores and grades even if the rest of the application is mediocre. Admissions officers at these schools notice the lack of genuine interest in the school, and this often leads them to reject the student as someone who clearly doesn't care about going there. Supplemental essays and "why this college?" essays exist to weed out these types of students.

If you want to avoid this type of confusing rejection, don't be arrogant and careless when applying to safety schools. They're going to notice, and they will be far less inclined to admit you despite your stellar academic credentials.