At the end of the day the person who had the authority to decide the facts decided that Brady "did it." That is what matters. Much as during a football game the "officials have spoken." Some people do not know when the game is over.
Problem is that sorry excuse for an "investigation" was one-sided, biased, and fueled by the 24 hour news cycle and envy of the Patriots' success. Your football analogy is more like the white hat having a $500 bet on the game he's working. Sure he's got the authority to make the call, but if he's doing it to further his own agenda, that is a reflection on the referee's integrity, not the players'.
The NFL never even tried to hide the fact that they were out to get the Pats from day one. Sensationalist media reports whipped people up into a lather, and we all know that in the court of public opinion, there's never a tall enough tree.