The PD also forbids Starfleet officers from interferring in the internal politics of another race. i.e. The Klingon Civil war.
The PD won't allow them to interfere with anyone's internal politics without permission, yes. When Km'pec asked Picard officially for aid he had to do it.
Also, keep in mind the greater context of the Civil War: Gowron was not recognized as the official Klingon leader at the time and for a culture as martial as the Klingons if he won the leadership because of Federation aid it would've weakened his stance after the war was over. Once it was proven the Duras were getting outside aid it destroyed THEIR position too.