This kind of logic could be applied to essentially anything that isn't a literal life and death situation. These young men and women spend more time with their coach, and more time at practice than they will with their parents, or their professors, or in any individual classes, over the course of these 4 years. By any external measure, the coach was doing an excellent job and produced both results and a positive team atmosphere. Who are you to judge how these young adults respond to a major shift in one of the most significant aspects of their current lives?
So you're saying the AD could have fired him for completely idiotic reasoning, but the kids would still have no cause to complain, so long as they're never told the reason for the firing?
If the coach actually did something inappropriate, its even MORE important that the reasoning for his firing comes out so he doesn't get hired somewhere else and get caught up in the same situation, as well as to ensure the misdeeds aren't being covered up from potential victims or others involved.
In my experience, college athletics is exactly the type of place where stupid crap like 'petty bickering with a colleague' and favoritism can run rampant in hirings and firings.