I've always been led to believe by reading various NFL pro analyst commentaries & reviews, (Cowher, others) that Clark Hunt has always played a major role with important decisions related to the Chiefs, rather never gave Pioli "full control". One incident proving this is when Jeff Fisher flew to Dallas last year reportedly for a coaching interview. The meeting was in Dallas with Clark Hunt & Scott Pioli present, not in KC with Pioli only.
In the one on one interview NFL.com recently did with Clark Hunt...Clark confirms that he has always been involved with Pioli & football operations, which would include coaching hires, draft choices, & so on. The only real change Clark is making, is that from this point forward, the HC will report to him and not the GM, whether it remain Pioli or someone else. Clark also states clearly in this interview, that he could retain Pioli, as well as not, based upon many factors.
The entire article can be read following the link below, but here are points I'm referring to above;
NFL: "When you say the coach and GM will report to you, does that mean you'll be taking a more hands-on role in football?"
Clark: "I think it'll be a different role. I do spend a lot of time already on the football side. Most of that interaction in the past has been with the GM, as opposed to the head coach. On a going-forward basis, I anticipate spending a lot of time with both."
NFL: "Do you feel like Scott Pioli can still be the right man to right the ship here?"
Clark: "I have not ruled that out. We're still evaluating that. But the priority here over the next few weeks is going to be the head coach."
Clark Hunt discusses Kansas City Chiefs' new direction - NFL.com