> the very definition of "people who work well together" is that they are productive, and the definition of "don;t work well together" is that they aren't.

I don't agree.

Working well together suggests they cooperate to reach a common goal, regardless of their individual productivity.

Not working well together suggests that they might even waste their time attacking each other instead of working towards a common goal, which has a negative impact on a project regardless of how productive each individual might be.