No one should think that the NFL actually cares about a just outcome here. Hell, I would argue that they don't care about the outcome at all; they just care about being perceived as taking a hard line against what can be broadly defined as "player misconduct." It may be true that including Brady in this was a titanic mistake the NFL, but they are now dug in and cannot back down.
In summary, they are leaking because they don't care about the court case. They need the public to know that there will be no settlement without Brady accepting the power of the commissioner's office to discipline him. If their action causes Berman to vacate the suspension, they simply move to the next step. But that's fine, because this was never about Brady in the first place.