The thought is if USC moves to the Big 12 that could open the door to some movement with the Big 12. I don't think anyone is holding their breath, but there's a chance it would affect BYU.
The better scenario for BYU is if a few blue blood football programs went for independence together. If Texas, USC, ND, Oklahoma, and BYU were all independent, suddenly the landscape is changed. Independence could upset the ridiculous conference system we're in now. Schools that are being held up by a conference like Iowa State, Vanderbilt, Rutgers, and Utah would drown, and schools that are carrying their conference might thrive.