This is how it works in the United States military and I'll start at the top. The Commander in Chief (the President) delegates his authority to the next senior officers. Then those officers delegate their authorities to other officers down the chain of command. By the time you get to the individual unit level, there are usually quite a few delegations. Most of them, if not all (I'm not privy to anything above the division level), are in writing. What this effectively does is allow the individual unit commander to act on the behalf of his superiors.
Do not confuse authority with responsibility. Responsibility cannot be delegated. So, in essence, the superior is responsible for the actions of his delegates. There's a problem in the United States military. It concerns officers that act outside the scope of their delegation of authority. They get caught but the general public doesn't usually find out about it unless someone tells the media. It's happening more and more often and you're starting to see more of it being publicized.
So who's responsible when the officer acts outside of their delegated authority? By acting outside of that authority, that specific officer has decided to act on his or her own authority and is now responsible for his or her own actions. Let's take the case of that prison in Iraq. Whether the officer in charge of that facility was acting on delegated authority or not, we will probably never know. I can almost guarantee that someone in the chain of command was acting outside his or her scope of authority.
I know that Bush-bashing has turned into a favorite pastime for a lot of people, but do you really think he's responsible for everything that happens? As the Commander in Chief, he is only responsible if what happened was performed within the scopes of delegated authority. Otherwise, he is not. It's really difficult to explain this to people without a military background in a way that can be easily understood, but you can't fault a guy for trying.



