I'm not totally a Parcells fan, but I think the one thing Parcells KNOWS is how people identify and relate to him. He openly told Jerry Jones, "I'm not for everyone" and if "We don't win, and win fast his coaching style wouldn't go over very well".
Parcells is a hard ***, that sort of picks and chooses when he wants to be a hard ***. He might let player who is a hall of fame talent get by with a lot, and cut a marginal player for a minor transgression.
He didn't want to deal with problematic players because he would only take so much from a player before he took some sort of drastic action. I think that is why he referred to T.O. as "The Player" generically, and avoided dealing with him. He let Jerry do the hand holding with T.O. and avoided dealing with him as much as possible.
Bringing in T.O. was a mistake. I don't know that much about the Woodson deal, but if a coach really doesn't want a player due to a personality issue, forcing the issue is generally a bad idea.