To underscore here -- the NFL has no right or power to do those things because they failed to bargain for that power in the most recent CBA. If the NFL wants to be able to compel players to turn over evidence and punish them for failure to comply with such requests, they need to bargain for it.
For not having power, it seems they made an example of Brady pretty much at will. I know Kraft is mad, but face it, a lot of owners probably love watching him squirm, and I see them backing Goodell who serves at all the owners behest. The Pats are generally seen as cheaters who got away with it, recall the play stealing scandal perhaps? I live well outside of Boston and people here in Cincinnati are loving it and posting stuff on facebook about how great it was Brady got caught, being a C's fan I kind of like the Pats, I defintely do not like the Bungles (Bengals).
But I still the NFL as a whole as a lot more powerful than you. They are not bound by law. They can do whatever they want as long as the owners stick together.