The innacuately reffered to "non-interference policy" mentioned in TNG Redemption, was sited as why the Federation could not become involved in the Klingon Civil War, because "It was an entirely internal matter" but the argument stands is that (this is what is really called) policy of non-interference is just a desciption of a hefty chunk of Prime Directive which in it's totality covers a lot of ground that was irrelevant to the Klingon Civil War.
WORF: Captain, we must intervene. The Duras family is corrupt and hungry for power with no sense of honour or loyalty. They represent a grave threat to the security of the Federation. Captain, you and I know that they have conspired with Romulans in the past. If they should be victors in this war, they will surely form a new Klingon-Romulan alliance. That would represent a fundamental shift of power in this quadrant. Starfleet must support Gowron. It is in the interests of both the Federation and the Empire. I beg you, support us in our cause.
PICARD: Mister Worf, I don't have to lecture you on the principle of non interference. As Starfleet officers, we have all sworn an oath to uphold that principle whatever our personal feelings. I'm sorry. I must refuse your request.
GOWRON: By right and tradition, I am the sole leader. All who oppose me are traitors.
PICARD: I understand your position, but I', sure you're aware that the Federation cannot interfere in what is, by definition, an internal Klingon affair.
GOWRON: You arbitrated the Rite of Succession. You are already involved.
PICARD: My duties in that regard are finished.
"Principle" is a weird word to use for a regulation in the Star Fleet Rule Book. Also note that Picard was allowed to interfere in a Klingon/Romulan war, so the non interference policy only extends to the goings on of one planet or one species and what they get up to on their own time, and how they evolve as a culture on their own time table, which does sound a hell of a lot like the prime directive if it accounts for after the invention of warp drive WHICH IT DOES.
Just because some one asks for Sanctuary, a Star Ship Captain doesn't have to give Sanctuary (I think that priests do, no matter what.) wich is why Janeway had that trial for Quinn in Deathwish.