How do med schools view premeds taken at colleges other than one's undergrad institution?

In late 80’s, I applied as a nontraditional student without a committee letter. In fact, I didn’t even know such a thing as a committee letter even existed. Didn’t keep me from getting in just about everywhere I applied. I’m just asking if anyone has any knowledge of this. I just found out that one of kid’s schools is apparently cutthroat and grade-deflated, and besides, kid wants to double major in two non-science majors. It occurred to me that this might be the best way to do it - kid would get to take the best classes, with the best professors, squeeze the best possible out of that T20 school, and get the slog premed sciences out of the way in the summer at local state U. It would probably add another 12K to the total cost of college.