In the absence of any other information, I'm sticking with my theory that the bottom-line is that BA refused to conform to what are now widely-accepted workplace conduct guidelines.
That's the whole point, with no actual information, all we can do is come up with our own theories, which can get into dangerous territory very quickly. Who knows what actually happened--we may never know. But it wouldn't surprise me if he said something somebody didn't like, but "refusing to conform to what are now widely-accepted workplace conduct guidelines" can mean a bunch of things, some more forgivable than others. If someone refers to another person as "Oriental" instead of "Asian," that would fall under the "modern workplace" rules, but is it really that offensive to cost someone their job and blow up the whole season? I'm not saying it was as trivial as that, and I have to agree with the theory that whatever it was, it must have been pretty bad for them to take such serious action. It would be nice to have at least some idea. Another theory is that a passerby heard him perhaps yelling at Williams in an "inappropriate and offensive" way. Without any context, they reported it and when asked, Williams verified that it happened. For whatever reason, it blew out of control and any chance of mitigating it would have been seen as sweeping it under the rug and turning a blind eye to bad behavior. And that would have left them open to liability.
What I'm suggesting is that it may not have been something 'pretty bad', but just repeated instances of things just 'not acceptable' in which he wasn't willing or wasn't able to modify his behavior. I base this on the fact that, even though almost everyone agrees that he can be stubborn, abrasive and arrogant, people really do respect and want to work with him for the most part. When things get escalated to HR, more oversight/monitoring and restrictions get applied - and I can see him getting irritated and resentful over that and just getting less and less cooperative with that oversight. So, nothing solid to base it on, other than I just don't see him doing something so horrible that it would require him being forced out, one way or another. I think it's much more likely that he's used to doing things his own way and felt that's what he was brought in for and wasn't able/willing to put up with guardrails imposed by HR (or the equivalent).