This is simply not true. You may have those rules at your company, but there is not federal law that mandates such. In Pennsyvania, I can fire any employee at any time for any reason I want (assuming that the reason is a discrimatory one covered by federal regs, ie age), and the employee has zero recourse. I can absolutely keep track of an employee digging their own grave and fire them when I have had enough.
Lets also not forget, in TO's case, this is not the first time he was warned. He was sent home from training camp for a week for being a jerk and telling his coaches and teamates not to talk to him. Around that time, the Eagles sent a letter to at least TO and his agent (probably the NFLPA as well) outlining the reasons he was sent home and what would be expected of him when he returned. During this same timeframe, TO publically announced on several occasions that he would return to the team but he was going to be a disrutption. He has proceeded to do exactly that. He was almost certainly given a number of verbal warnings (I have nothing to back this up, just speculation here) between that time and now. Finally after his latest outburst, he was given two options, appoligize to those that you have attacked in the press or you will be removed from the team. He chose to play a game, calling the Eagles bluff, and appogized to those he felt like appoligizing to, disregarding specific instructions his employer gave him. Willful misconduct? Probably just plain stupidity, but nonetheless he had full control of his future and he chose the path he would take, not the Eagles.
I cannot see how the Eagles are not well within their rights to deactivate the guy for the rest of the year.