If it can be shown that there were allegations and punishments handed down at LSU that were lied about or not disclosed, I think they can have a good case to let him go based on events that occurred previously. In medicine, if you lie or fail to disclose criminal incidents from the past, it can result in forfeiture of your license and can cause a hospital to release you from employment based on falsification of information. So, it would not be unheard of. If it is just based on rumors, then that is likely unfair.
Full disclosure, I have not read much on this about what he actually did at LSU and whether it was criminal or if he received actual official punishment.