@Crell My favourite "dropped into fix a project" story had three warring groups like this.

The group manager was a nice guy, bright. But he'd been promoted based on his engineering skill with zero management training and given a major project. He was way out of his depth and as you say, effectively incompetent.

I *independently* convinced each group that I had their best interests at heart and showed them the spec I wrote "just for them." Each of the three signed off on separate copies, then when we had yet another panicked "this project is going down the toilet what are we going to dooo?" war room meeting, I suggested that since we now had a common spec, we should instead get to work.

We did. Delivered the project just a few hours before deadline.