The whole thing boils down to Political Correctness
No. Not at all.
Seriously, read what happened. Yeah, BBC has done plenty of bone-headed things in the name of PC. This, however, is not one of those things. Clarkson punched a staff member. He admitted to doing it. Physical assault is very clearly a violation of workplace terms there. Hell, if you punched a coworker at your place of employment could you reasonably expect to keep your job? I'm quite sure I could not and I am not nearly as highly regarded (or highly paid) as Clarkson.
This ended up being about the fact that the same rules need to be applied all through the pay scale. Just because he is a celebrity, and a host of the most watched television program in the world does not mean that rules do not apply to him. Hell, if that had happened here in the US, he'd be facing a multi-quintillion-dollar lawsuit already.