Sorry, Bob. Usually enjoy your stuff, but reading this just hurts.
The feds? The colloquialism is typically used for federal agencies, like the FBI, DEA, etc. This procedure ain't that. The 'feds', as you call them, would be the NFL/defendant, not the court overseeing discovery procedures and procedures (the federal court rules on discovery disputes when documents and answers are withheld). If you are remarking on appropriate strategy, then you probably need to research the rules of the game.
At issue would be discovery rules. While civil rules permit broad discovery in contrast to criminal rules of discovery, they do not permit fishing expeditions into irrelevant matters. As you appear to note the issues would be limited by arbitration procedures, you appear not to grasp the principle that relevancy is limited to the issue in question. Narrow issue, narrow discovery. Your conclusion doesn't follow. Broad issue, lots of discovery. Narrow issue, limited discovery.
Having participated in a bunch of arbitration proceedings in federal court, the parties would likely participate in legal argument directed to the authority granted by agreement, followed by attacks on the NFL under the limited theories permissible in the presence of a valid arbitration agreement.
Capitulate now? To what end? Brady may never clear his name, but giving up sure doesn't look like the actions of an innocent man. Your J. Edgar Hoover-type theory that this process may somehow unleash the skeletons from the Pats/BB/Brady closet is pure conjecture, and suggest you think little of the Pats and their practices (ie., they have dark secrets to hide and are better served keeping them buried).
Plenty of reasons to battle. None compelling that I can think of to back down, other than the possibility that Brady could sit out playoff games if the federal process is badly timed. Even then, I would happily watch Brady spank Roger even if that costs the team playoff success. He has more than earned his right to protect his name, having given up plenty for the Pats in his career.