I absolutely don't think people get rejected from "low-tier" schools because they are "too good." From what I've seen, there are three main reasons a low-tier school will reject a high stats applicant:
1. The applicant is clearly disinterested--e.g. secondary essays are weak, goals outlined in PS don't fit with the type of student a schools tends to accept (see #2), etc.
2. The school's mission is not a fit with the student's profile. For example, a school that heavily emphasizes community service will not accept a student who has 2,000 research hours and 50 volunteering hours. A school that churns out rural, primary care physicians will not want a student who has never shown any interest in that type of medicine.
3. The school is a "safety" school that 12,000 people apply to each year. Think BU and Georgetown. This is the only instance in which high stats may be a slight disadvantage; obviously the volume of applicants to these schools are high enough that if they wanted their average MCAT to be 35, it would be. However, if you're truly and outstanding applicant that's a good fit for the school, you aren't going to be weeded out because you're too awesome.