Well, only those involved directly with the show would know the dynamics of exactly how things are done. Simon Cowell is one of 6 Executive Producers. There is also 1 Co-Executive Producer, and I have know idea what makes one of the 7 a Co-Executive Producer, and the other 6 just Executive Producers. As I understand it, the Executive Producers are those that finance the operation. they are paying for it to happen. Producers are hired to produce a show. Directors are the people more actively involved in the productions. "Getting their hands dirty" if you will. The show is then sold to a buyer, in this case NBC.
Now, what this actually translates to as far as who is deciding what can vary a lot. The executive producers have the final say as to what goes on, but they could leave it up to their producers as well if they prefer a more hands-off approach. With that in mind, the buyer, NBC could say, "we won't pick up your show if you do this," or "we will only air your show if you take this approach." The executive producers then have to decide whether to do what the network wants, or try to find another buyer, or negotiate a middle ground. If a Producer has a proven track record and is a hot commodity (maybe Simon Cowell fits this description?), then there may be several networks wanting to buy they show, so they basically have to let them do what ever they want with the show if they want to have it.
The short answer to your question is, I don't know, it depends.
Hope that helps.