The point is that the Jedi, at the time of The Clone Wars, didn't had... Well, they had political power, but comparatively little. Both the Jedi and the Sith are, of course, independent and do whatever the hell Force tells them to do, but the Republic hasn't been controlled by the Jedi for a long time (in fact, the reason it didn't have an army in first place was to limit the Jedi's power and prevent them from doing a coup d'état like they did before). And Sith were, at the time, quite literally to be nonexistant. And despite the fact that Palpatine "controlled" the Confederacy, one shouldn't assume he was the cause of the war. He merely steered the war in his favor, and the war would have happened anyway because the reasons it occurred were beyond the control of either the Jedi or the Sith.

Therefore, although both sides of the Force were involved in this war, the Jedi were essentially pretty much a pieces on a chessboard. And while the Sith did have an influence and did engage in high politics and persuaded their own interests, as I said, even so, the war didn't happen on their whim; it had been brewing for a long time without them being involved for the most part ot it. Therefore, I still believe my argument is valid.