There's a distinct difference between criminal proceedings and what happens in the NFL though.
The NFL has something called conduct detrimental to the integrity of the game/league that all of its employees are held accountable to. Unfortunately that term is also very vague and nebulous. In the case of Tom Brady, he was named to be involved in this "scandal" by other parties involved, however his conduct during the investigation did nothing to exonerate him from being involved. Sure, it wasn't proven that he was actually involved either, but there was enough circumstantial evidence against him in the court of NFL arbitration that lets him fall under the category of conduct detrimental to the integrity of the game/league.
Simply, by not presenting the proper evidence to support his defense in this case, Brady just made the presumption of guilt that much greater. Remember, this isn't a court of law - this is collectively bargained arbitration. The NFLPA agreed to it and the NFL holds the cards here. It doesn't work the same as your traditional legal context anymore.
I agree that Brady, as an employee is not be held to a standard equal to that as a court of law. The NFL is after all an employer. But as you point out, the employer has signed with the NFLPA a contract. That contract does set certain standards in place to ensure that the employee receives greater consideration, than if no contract were in place. The statement by the NFLPA [below] that I find most intriguing is the accusation that the NFL violated the plain meaning of the CBA.
I believe this has to do with the NFL front office's process of passing judgement on Brady and the subsequent appeal process. As I've heard, the Commissioner is responsible for passing judgement with fines and suspensions. But the player has the right of an appeal with an independent arbitrator. What Goodell did, was to delegate the initial review process to his second in command, and set himself up as an independent arbitrator. That I believe is what the NFLPA says he cannot do, according to the plain language in the CBA.
Regarding the smartphone, I haven't heard if this phone and its service, was paid for by either the NFL or the Patriots. If so, demanding the physical phone for the investigation seems reasonable to me for the purposes of the NFL investigation. But if it is a private phone, I don't see how the NFL can reasonably demand it. We cannot compare Brady's phone to say Clinton's email, as the latter was conducting government business on her private server.
I think that Brady stands a good chance of the court agreeing to hear the case, and ultimately sending it back to a true independent arbitrator, who is not employed by the NFL front office. In other words, this might not be resolved for a long time. Getting an injunction to delay the suspension might be a higher bar for Brady's lawyers to overcome. So we could be reading about this finally being resolved 2-3 years from now.
"Statement from the NFLPA:
“The Commissioner’s ruling today did nothing to address the legal deficiencies of due process. The NFL remains stuck with the following facts:
• The NFL had no policy that applied to players;
• The NFL provided no notice of any such policy or potential discipline to players;
• The NFL resorted to a nebulous standard of “general awareness” to predicate a legally unjustified punishment;
• The NFL had no procedures in place until two days ago to test air pressure in footballs; and
• The NFL violated the plain meaning of the collective bargaining agreement.
The fact that the NFL would resort to basing a suspension on a smoke screen of irrelevant text messages instead of admitting that they have all of the phone records they asked for is a new low, even for them, but it does nothing to correct their errors."
http://boston.cbslocal.com/2015/07/...-to-take-deflategate-appeal-to-federal-court/