There are enough private schools to go to if you're a public hata. All but 2 of the 24 schools I applied to were private. Plus, state schools are usually rated less highly, so if you are so obsessive to care about the state thing (like the URM thing, ad nauseum) then you are probably obessive enough to have outrageous grades/MCAT and get in to a higher ranked, private school. Most people don't want to go to state schools outside of their state, except maybe in Cali and at U Mich. If you speak of the reduced tuition, well, residents (and their families) pay taxes to support the school. As a resident staying in the area to go to med school, you are more likely to stay for residency and practice in that area. At state schools, you are also more likely to go into primary care. There is favoritism along those lines as well if you interview at a state school.
I'm going to U Mich, and I am a resident. U Mich is weird because they take more non-residents than residents. Even when they do take residents there, they have exceptional numbers and personalities because there are many high achievers there already, like at U Mich undergrad. U Mich and UCLA are the two schools with the MOST pre-med undergrads in the US. I didn't go there for undergrad, however. I will say that even though I applied to schools ranked higher than my state school, I'm giving preference to my state school in great part because of family reasons. I know that if you tell most schools, public or private, that your family is in the area, they will give special consideration.
Do you have a school you are applying to out-of-state that is public? If so, what are your reasons?