I am not an expert on the subject, but I would be surprised if there aren't clauses in his contract allowing him to be dismissed on public relations or behavioral grounds. Additionally, I believe most athletic departments have the football trainers/doctors structured as a separate department not under the football coach's jurisdiction, and coaches have to sign waivers/statements indicating they will follow directions and look out for well being etc. If the trainers testify — as they apparently did to the AD, who just fired Leach — that Leach didn't follow their directions, he's not going anywhere at trial. I note his lawyer spent a lot of his time trying to indicate Leach didn't specifically violate medical prescription so I imagine that's a real legal issue.
Basically it boils down to the fact that we all hear about players being suspended and dismissed from teams and schools for disciplinary reasons, apparently without generating lawsuits. Why would a coach be any different? I've seen first-hand a positional coach get fired by a head coach for the way he dealt with an injured player.