What Bush said was, "Where mistakes have been made, the responsibility rests with me."
Let's say you're a department head, and you steal from the petty cash drawer at your office. Your boss notices the missing money, and he calls you and your whole staff in, and demands to know who stole the money.
And you say, "Where petty cash is missing, the responsibility rests with me."
That's very different from "I did it. It was a mistake, and I'm sorry."
It's the difference between your boss thinking you're covering for someone (what a guy!), and his knowing you're guilty. It's the difference between evasion and owning up.
It's the difference between a weasel and a man.
(And by the way, Bush left out an important part of his plan. He hasn't been able to win with hundreds of thousands of soldiers, so what good will 20,000 more do? Simple: These will be 20,000 Terminators, Borg, CHUDs, and X-Files Super Soldiers.)