Also, I think there is a difference when Omaha kids think about their next step in life after graduating high school. When kids graduate high school, a lot of kids are looking "for something bigger" regardless of where you grow up. For Omaha kids, that "something bigger" is a school in a state super far away from Omaha. For Omaha kids, going to UNL is a "lateral move", and going to a small school like UNK, Hastings College, Doane, etc. would be a "step down". For kids outside of Omaha or Lincoln, going to UNL is the "something bigger", and going to a smaller state school would be the "lateral move".
Also, just because Omahans may have stereotypes of people who live outside Omaha and smaller Nebraska cities/towns, doesn't mean that non-Omahans don't have negative stereotypes to Omahans and the city of Omaha.