I agree with you. But I suspect the reason they need to shut up is because their actual reason for firing him is not justifiable enough to protect them, and stating it now would just give more ammunition to plaintiffs. If they had him caught red-handed in an actual crime, or even a clear ethical violation, a good lawyer would be communicating that to the press on their behalf.
High-ranking employees that have communicated with them have already said they have admitted it wasn't due to any security, safety, privacy or financial concerns. So there aren't a lot of valid reasons left. They're not talking because they've got nothing.