but she allowed herself to be manipulated into winning, and that's the next best thing to being powerful enough to do it yourself

I would argue, when I came right down to it, Katniss managed to get both her AND PEETA out of the games herself. Yes, Haymitch and Peeta helped her get to the end, but she was the one who figured out how to get the Capital to have two Victors instead of just one.