Jacobs Hired Pearl. He is heading out the door. The barn would never hire Petrino.
If it were an Athletic Department at a school within light years of being normal, I'd agree.
But the nominal Athletic Director (Jacobs) didn't hire Pearl any more than you or I did.
Jacobs doesn't (didn't) wipe his nose without checking with Pat Dye first. Who just happens to be the fired cheating coach for whom the field is named. You can bet Dye checked in with Bobby Lowder before getting back to Jacobs.
Ordinarily, your logic would be 100% sound. But you're dealing with The Mad Hatter (Dye), the Cheshire Cat (Lowder), and the Queen of Hearts (Jacobs).
Logic just doesn't apply in either Wonderland or Auburn.