I think good players want to play well all the time, regardless of any rumours they might be hearing about trades or whatever.
These guys are conditioned to tune it out, it's part of the job. Sports psychologists abound, as do veteran players with sage advice.
If Cozens was letting it affect his game in some way, then that's on him for being immature.
I don't put much stock in it any of it. I think he's just not the player we thought he was.