Sure, maybe if the Sona had decided to do that without the federation, but as soon as the federation was part of it, the Enterprise had to be part of it as well.
There is some precedent. In "Ensign Ro", the admiral was secretly meeting with the Bajoran rebels, bringing Starfleet into the conflict with the Cardassians. Picard could have said "not my mission, not my problem", except they had to solve it in the same way they had to solve the Baku conflict because Data was what brought them there, making it their problem now.
In theory, they could have gone straight to Starfleet HQ and tell the high command what they were trying to do, but they didn't have time because the Sona was already attacking. The whole thing with them going younger was dumb, but they did have a lot of justification for intervening. Ain't hte first time the crew has done stuff like this in TNG canon.