I'm not sure if this is what you mean, but what I heard is that the most common task of management consulting is to sell an already made decision to the rest of the company. The consultant appears neutral and is expected to have good presentation and sales skills. The analysis technique and inputs can be chosen to yield the desired result. The more expensive the consultant the better for credibility. So it's obviously a great way to make money.
The principal-agent problem is thus between the company and the person hiring the management consultant(s).
Backfilling a CEO idea happens sometimes. And that's not bad per se. They still need to see if their idea holds water, and consultants have great presentation skills that the CEO can leverage trying to explain the idea to stakeholders.
But most of the time, at least the top consultancies, they will call out stupid ideas. They have their own reputation to keep and shareholders, the guys actually paying for the party, don't usually like being made fools constantly.
Or, most commonly, be hired to shed some light on a bunch of seemingly equally good ideas. Business strategy issues hardly have black or white and sometimes the recommendations fail. People in the company make sure to publicize the consultancy involvement as a cover your a strategy, but hardly share the credit when things work.
About the parent comment on principal-agent problem. He must be a management consultant for throwing a buzzword around in a discussion and dropping the mic :)
