I don’t know why people are so surprised that school name matters. It’s the same thing for med school admissions: if you go to a top undergrad (or even Harvard/Stanford/Yale/Princeton/MIT), you will have a lot easier time getting into top medical schools than someone with a comparable application but went to a no name undergrad. The fact that med school name matters for residency matching should not be of any surprise, seeing that networking and letters play a major role.
Top med schools have much higher quality students on average because admissions at these schools actively select for superstar applicants who will become leaders in medicine. The nature of competition in getting into top schools is more intense and more selective, with applicants having amazing applications.
School name matters and going to a top med school will help a lot for matching into competitive residencies and fellowships. Program directors know the high quality of students coming from top schools, and so students at top schools can match comfortably even if they have no research output. School name alone is enough to stand them out.
Unfortunately, the same does not apply to students at low tier schools, so they need to work extremely hard, get AOA, destroy Steps, destroy clinical years, get strong letters etc. in order to match into competitive residencies. It is not easy to match into a top residency program just like it’s not easy to get accepted into a top med school. But hard work does and will pay off.