The Federation has never been shy to interfere. In TOS, they forced themselves upon the Eminians, sought mining rights from the Capellans, said they'd huff and puff until they got to speak to the Melkotians... In ST:INS, they decided to relocate an iron age settlement without asking anybody for permission.
Just like Pavonis
says, it's Starfleet
that is kept from doing such things by the Prime Directive. If the civilian government tells them to interfere, they will. If the government doesn't tell them to, they are not allowed to.
It's a pretty good idea to keep the military out of politics...