Yeah, rookie move on his part. The fact that he does not have an established disciplinary arbiter lined up on retainer, given the large amounts of general fuckery that go on in the NFL off the field, is borderline negligent on his part.
The NFL played the wrong angle here, though. The right argument to make, if you want to discipline people, is to state that as an entertainment service that cheaters, wife beaters, and dope heads are bad for the brand. I am pretty sure if Jarred somehow got cleared and then tried taking Subway to court to get his job back he would be laughed out of the room. So, basically even though you cannot prove Brady is a cheater beyond all shadow of a doubt, the public perception that he is damages the NFL as an entertainment brand if he is not punished. AP took a switch to his kids nuts might be legal, but having a literal kid ball buster front line a team is not good for the NFL brand either. This would shore up a lot of bullshit, actually, but require pretty much equal enforcement or accusations of bias would be a major issue.
I don't think classifying sports as entertainment, legally, would go over too well in certain circles, however.