Going to HYPSM vs going to other top 20 undergrads won't matter at all. The only time it might matter a tiny bit is, for example, that a 4.0 at Harvard carries more weight than a 4.0 from a community college, but either way your MCAT will provide a standardized metric for your academic abilities. No adcom is going to automatically turn someone down for attending an obscure college if they scored 520 on their MCAT or something. I have met several people on the T20 interview trail from smaller schools or even colleges that I had never heard of before, so they're clearly doing alright for themselves despite not attending HYPSM.