Then again, "The Circle" explicitly equated noninterference in internal affairs with the Prime Directive:
Chekote: "But internal to Bajor. The Cardassians might involve themselves in other people's civil wars, but we don't. The Prime Directive applies, Ben.
The situation appears identical to that of the Klingon civil war: Starfleet knows outside agents have an interest in the outcome and may be meddling already, but as long as the declared combatants are from one and the same culture, PD says hands off.
But since there was no defense pact between Bajor and the UFP comparable to the Federation-Klingon alliance, Sisko had to go rogue despite the knowledge of Cardassian involvement.