As I understand it, there is a public university board in North Carolina that oversees both UNC and NC State. They basically share board members. They've pretty much always been tied together as a package deal in that the board won't approve one leaving the other behind.
This is somewhat similar to how Texas Tech got into the Big 12. The Texas governor was a Texas Tech grad at the time that the Longhorns were leaving the old Southwest Conference to join the Big 12. The Texas governor demanded that the Longhorns take Texas Tech with them. Funny how Arkansas turned out to be the school that made the smartest moves when the old Southwest Conference started falling apart.
This is also what stopped the PAC-16 deal back in the late 2000s. Texas legislators were mad Baylor wasn't included and it scuttled things.