There are two main reasons the NFL is acting as it is:
(1) Primarily, the NFL is trying to send a signal to players - or anyone else - who challenges them legally. The more litigators the NFL hires, the more Brady's team might have to hire in response. If the NFL can cost Brady three or four million in legal fees the NFL will be happy: they will have sent the signal to future adverse litigants that it is very expensive to sue them. The NFL is just trying to discourage future litigants, sending a signal that they will litigate endlessly, and expensively, no matter what.
(2) Secondarily, although Berman's opinion will not be overruled as such, very good attorneys lessen the chance that the language of the appellate opinion will set a precedent that will constrain the NFL going forward. So the NFL lawyers will work to make sure the appellate court narrows the scope of its opinion to the exact facts of this particular case.
(1) Primarily, the NFL is trying to send a signal to players - or anyone else - who challenges them legally. The more litigators the NFL hires, the more Brady's team might have to hire in response. If the NFL can cost Brady three or four million in legal fees the NFL will be happy: they will have sent the signal to future adverse litigants that it is very expensive to sue them. The NFL is just trying to discourage future litigants, sending a signal that they will litigate endlessly, and expensively, no matter what.
(2) Secondarily, although Berman's opinion will not be overruled as such, very good attorneys lessen the chance that the language of the appellate opinion will set a precedent that will constrain the NFL going forward. So the NFL lawyers will work to make sure the appellate court narrows the scope of its opinion to the exact facts of this particular case.