> Having strong analytical skills seemed essential

and

> they have a knack for corporate maneuvering

One way to view this is that the above combination of skills is both rare and very useful. That means it's expensive. So instead of hiring someone like that at "full rate" and keeping them around, you can "borrow" them from McK to solve a problem your regular crew can't (or isn't able to) for various reasons.

Plus, as one manager of mine said many years ago:

"We use consultants b/c they are both easy to hire AND easy to fire"