Not exactly sure this is entirely true. Med school do look at where you went to undergrad, but mostly to make sure that your undergrad is a 4 year institution and that it has been properly accredited. They also look to be able to place your application is context. (Prof said best chem student in 10 years–10 years at a large state university is different than a 10 years at a small regional campus that produces mostly business and agriculture grads.) They may also consider if that college/univesity has sent students to their school before and how well those previous students have done.
Med school adcomms really don’t consider a undergrad’s USNews ranking at all. It’s irrelevant.
But @thumper1 is right. A graduate from UTK is not going to get the nod over a student from Bama just because of that’s where they graduated from. The “everything else” of the application is 1000x more important.
If you look at the profiles of matriculating students at various med schools, you’ll see students coming from a wide range of undergrads.
W/R/T picking an undergrad–choose the one that makes most sense to you. The one you like better, has the best fit, offers you the widest ranges of options (in case you decide against med school–and most people do), and/or makes your parent the happiest.
Whatever choice you make won’t be what keeps you out of med school.
The one advantage I see of attending an in-state public university is that school has typically sent its grads to the state med schools and are very informed about its requirements and expectations. An advisor at the state U probably has a better grasp of what it takes to get accepted into the state med school than someone at OOS college. The med school adcomm will also be more familiar with the various professors at the local state U so their LORs may carry more weight. (But only at in-state med schools.)