It’s the “some kids” that is the key.
@GWYalie1994, not sure if I am reading your post right, but most on CC know that Yale does not favor ‘normal rich’ kids with connections, and that there are students from a range of economic backgrounds at both places. However, Yale promises to meet ‘full need’ of admitted students and GWU does not, and debt is a bigger part of the package at GW (and NYU and American) than at Yale.
Schools like Yale and scholarships like the Robertson (UVa) or Morehouse (UNC-CH) are lightening strikes for all students, including this highly-qualified OP, simply b/c there are so many outstanding applicants. For a student with limited finances, and a med school goal, finding good options that result in little (or, better) no debt is the goal. Given the OPs options, schools that are known to be more restrictive with financial aid, and/or that use loans more heavily, are less attractive. Similarly, most of the state universities you list are not good options for an out-of-state student: UNC-CH does meet need for OOS, but afaik, none of the rest of the publics you list give finaid to OOS students.
Your point that most Yale students are just nice, normal, hard-working, talented kids is completely fair, and one that few people on CC would argue with.