What If Withdrawl from Iraq Brings Peace?

From Tom Quiggin, Why Bush Has It Wrong, and why al-Qaeda needs us to stay in Iraq:

U.S. President George W. Bush has repeatedly claimed that if American forces leave Iraq, the war-torn state would be surrendered to al-Qaeda. It is unlikely that there is any basis in fact for these statements.

Al-Qaeda is likely to leave Iraq once American forces depart and when a new government (or governments) take over. For reasons of doctrine, history, and al-Qaeda's own assessments of the situation, it is unlikely that al-Qaeda is either planning or counting on a long-term presence in Iraq after an American withdrawal.

The U.S. has been wrong about everything else, why not this too?