of members of the union (as Brady suggested in his Facebook statement when his suspension was originally upheld by Goodell), how is Brady exercising his right to keep his cell phone private a failure to cooperate? The league can't condemn or punish a union member for not doing something that the league has no right to expect in the first place.

For a very imperfect analogy, a defendant in a murder trial is not being uncooperative when he exercises his right to not testify in court. Brady had a right to keep his cell phone private, per the CBA. So exercising that right can't be held against him.

(That's my limited and likely flawed understanding, at least.)