These are exactly the types of scenarios we looked for when our son was on the hunt. There are a few unique publics that might fall into that category too, but certainly not any large research based institutions.
Remember too that medical schools could care less about undergraduate “prestige.” they care about your grades, MCAT scores, volunteer experience, and letters. Medical school is EXPENSIVE and professional schools do not give need based aid or merit aid. It’s all on you and your parents. Spending money on an OOS large public really makes no sense if medical school is the ultimate goal.