I said this in the other thread - here's what I've actually observed: If you arb a player three times and he has a Patience rating lower than 99, he is going to walk to free agency.
I have not actually observed anything to show that if I win an arb at any time against a player, that he asks for more money next time, or is more likely to seek free agency in later years.
In other words, the only time I've ever seen evidence that a player is "ticked off at ownership" is if you arb him three times. And frankly, if you actually arb a player three times you don't really care if he sticks long term or not; if he's even a good player you're angling to get the comp pick when he walks.