What isn't often discussed is how hard it is to go from a no name school that isn't ranked highly to an elite school. At a non-elite school your recommenders may be unknown to the admissions committee, the 'level' of education these applicants receive can be questionable ("What does an A mean from this program and how does it compare to our class?"), their research experience could be weak, student visibility could be weak (i.e. their recommender isn't known in the field, and their student didn't do any sort of research that made professors at our school aware of them in advance), the courses they take may be weak compared to other applicants (i.e. their program doesn't offer as many advanced courses, compared to other programs) and so on. There can be tremendous risk in taking students from unknown schools or non-elite schools. It's much easier to accept graduate students from a similar elite school, with well-known recommenders, and a history of successful applicants from that came from that school that did well in said program. It isn't impossible, but it is an extra step these applicants have to overcome.