I'd imagine that something similar would happen to any number of planets in the Fed/Klingon border area. They can't fight each other due to the Organians so they tend to fight proxy wars. You probably wouldn't be able to supply the natives with phasers but you can teach them to build weapons of their own. A similar situation probably played out on dozens of planets.
You can actually imagine something similar happening in A Private Little War when Kirk is encouraging the Organins to rise up against the Klingons even though they have made it quite clear that they are willing to follow the Klingons instructions. Kirk knew that Kir had said he would do and he still committed sabotage that would be blamed on the natives. Federation first, natives second seems to be how the Prime Directive is interpreted in these situations. When you have a culture that hasn't had any contact with another spacefaring race (or government) then you can pull out the purer version of the PD.