Picard didn't have a leg to stand on once the Angosian government told him to butt-out.
Actually, Picard did have a leg to stand on.
Roga: Mister Prime Minister, with all due respect, you will have to force us. Or at least try.
Nayrok: Captain, you must do something. Call your ship.
There's your "bit of turbulence"
where the Prime Minister was more receptive to Federation intervention. Instead of offering the assistance to help reintegrate the soldiers back into society right then and there, Picard is willing to risk the deaths of thousands just so he can teach the Prime Minister a lesson.
I guess I shouldn't look too much into this. We are after all talking about the same character who praised Riker for not saving a little girl's life.