If responsibility is not balanced by an equal amount of authority---and vice versa---bad things tend to happen.
Example: The commander of Abu Ghraib prison, General Janis Karpinski, will be punished for the actions of her soldiers, even though she did not have the authority to stop it.
“The orders from occupation commanders in Iraq effectively made a military intelligence officer, rather than an military police officer, responsible for the military police units, the report said. This arrangement was not supported by General Karpinski, the report added.” (source)
Example: A certain world leader has the authority to start a war, but refuses to take responsibility to stop it once it was revealed that congress granted that authority under false pretenses. And he's arguing before the Supreme Court that the executive branch needs more authority without responsibility, like the ability to detain US citizens without any legislative or judicial oversight.
UPDATE 2004-08-11: After thinking about it, General Karpinski could have kept better tabs
on her troops. I'm no expert on military law, but I'd say the burden of proof is on her to prove that she was barred from overseeing her own troops.