I think it's just a product of a known rivalry and pandering to the fans.

If you took the head coaching job at North Carolina, you might throw a jab at Duke in your presser.

If you took the head coaching job at Ohio State, Michigan might come up. (Did Urban Meyer mention Michigan in his acceptance presser? I don't know.)

Etc, etc.

Personally, I think Mr. Stoops has much more important things to worry about than trying to be cute and earn brownie points with the fan base. I'd do that with some novel concepts like bringing in players, coaching them into ballers, and winning a few games. LOL