Rumsfeld and Responsiblity

CNN.com reminds us that last year,

In the middle of the controversy, Rumsfeld appeared before Congress and said he took "full responsibility" for what had happened, and he said he would step down from his post if he thought he could no longer be effective.

Bush then publicly expressed confidence in Rumsfeld.

What does responsibility mean? Does it mean that if someone below you does something wrong, you're responsible for the wrongdoing? What if the wrongdoing includes torture, rape, and murder, what does it mean to say that you are responsible?

Or does it mean that you will stay on as Secretary of Defense, even into a new term? And that only a few wayward enlisted folks should be held accountable?