Bullcrap. They certainly do. Ask any Korean from Cholla Namdo. For you to deny this reality indicates to me that despite a Korean American heritage, you don't know nearly as much about Korea as I do. I'd agree that these ethnic distinctions aren't particularly deep, or particularly racial, even though the history of Cholla runs contrary to Korean mythology. The election of Roh Moo Hyun in 2002 was a huge deal for Cholla.
That's not an ethnic distinction. And, if anything, to argue anything along those lines you'd have to go waaaaaay back. To the times of Samhan and Buyeo.