Call this a weird analogy, but can France impose its will on, say, Luxembourg should the latter need assistance? not really, since Luxembourg is a sovereign state.
So Picard had little right to impose anything. At best, he could offer help, but not force them to settle the dispute. And besides, even if the dispute had been settled there and then, if I were Picard i'd still send a report to the Federation Council and/or President saying "these Angosians can resolve conflicts quickly, but then they deceived us all the time. Not Federation material!!" lol..