I guess I need to be direct rather than just say ask Congress or you US attorney:.
1. Contracts that break federal antitrust law are illegal and not enforceable.
2. Point 1 makes it is illegal for UAL, UAR, AU, UF, UGa, UK, LSU, Ms State, UMs, UMo, SoCar, UTn, aTm and Vandy to join together to restrict hirings, ie labor market activity, at UF of any other member or non-member of the SEC.
3. You don't get to restrain trade and if you do, there are criminal and tort sanctions. The sanctions can include treble damages for the person harmed by your illegal actions conspiring to limit the market for hiring football coaches. Though the coach has to mitigate damages, still head coaching salaries are enough nobody wants to risk triple damages.
4. In addition the SEC is UF and aTm. Those are the big dogs of the SEC. They are the schools in the two biggest states, they are AAU members giving them academic leadership clout in the conference too.
5. So add in point 4 as I and others said earlier any consultation will go something like this:
Dr. Fuchs: We are hiring Chip Kelly.
Whoever is SEC commissioner, ie the little guy the schools hired to run the jock conference the schools put together: Yes sir.
But apparently UF is not hiring Chip Kelly according to this thread making this whole discussion moot.