I agree that the TU shouldn't have signed up to the non-disclosure agreement in the first place. It puts a barrier between them and the people who they were elected to represent, so they cease to represent their members and are, instead, only representing themselves...
So feel free to issue them with a very firm "No"
Anybody - TU or Management who feeds you a line about how "X unit doesn't care about you, so why care about them?" is just applying the divide and rule tactic. Don't listen to that !!!!!.