That process was the AD's unilateral investigation, which had hardly begun. He had every right, and indeed a responsibility, to suspend his employee while investigating--every employer does. I've done it often. When Leach refused to permit that investigative process to proceed, by his attempt to remove the matter to the courts, the AD had no choice but to fire him for his insubordination. Unless there is some explicit language in Leach's contract to the contrary, then the AD did what he had to do to retain authority over his staff.
In other words, at that point the issue no longer was whether Leach acted improperly toward the student but now was whether he acted improperly toward his boss. No employee who is not protected by a contract can, or should, win that fight.
All the “administrative” explanation in the world can still not make that AD look like anything but a dummy. The entire situation is absurd. Firing a coach because he won’t apologize to some kid?
What soft little creatures some kids are now. Our high school coaches used a thick paddle on their guys if it was needed. Nobody thought much about it then, including the parents.