Rice, Iraq, 9/11

Condoleeza Rice did the Sunday talk shows in the US yesterday. I read the transcripts and her line on Iraq's relationship to 9/11 stood out:

With Wolf Blitzer on CNN:

QUESTION: Did Saddam Hussein and his regime have anything to do with 9/11?

SECRETARY RICE: Saddam Hussein, and we have said this many times, as far as we know, did not order September 11, may not have even known of September 11. But that's a very narrow definition of what caused September 11. If you think that what caused September 11 was that the people who flew airplanes in caused September 11 then, no, Iraq has no relationship. But if you think that this was a broader problem of an ideology of hatred, of terrorism becoming an acceptable means in places where there was a freedom deficit and there was no possibility for legitimate political discourse, then you realize that you have to have a different kind of Middle East. And a different kind of Middle East with Saddam Hussein at the middle of it is unthinkable.
With Tim Russert on NBC:

QUESTION: Let me turn back to Iraq. The war now in its fourth year and these are the grim statistics: U.S. troops killed, 2,316; wounded, injured, 17,271; Iraqis killed, an estimated number of 30,000; 130,000 American troops on the ground. When you were planning the war, some three and a half years ago, did you have any idea that three years into the war, those are the numbers that you would be confronting?

SECRETARY RICE: Well, I certainly thought that it would be difficult. I don't think anyone knew precisely what we would be facing in terms of numbers. And, look, everyone of those deaths is mourned by people in the Administration because these are families that have lost husbands and wives and daughters and sons. But we also know that nothing of value is ever won without sacrifices.

We're in Iraq because the United States of America faces a different kind of enemy and a different kind of war and we have to have a different kind of Middle East if we're ever going to resolve the problems of an ideology of hatred that was so great that people flew airplanes into buildings. Iraq was -- Saddam Hussein's Iraq was a threat. Now that --

QUESTION: But Saddam was not related to flying airplanes into buildings.

SECRETARY RICE: No. And we have never said that Saddam -- Saddam was not related to the events of September 11th. But if you really believe that the only thing that happened on September 11th was people flew airplanes into buildings, I think you have a very narrow view of what we faced on September 11th. We faced the outcome of an ideology of hatred throughout the Middle East that had to be dealt with. Saddam Hussein was a part of that old Middle East. The new Iraq will be a part of a new Middle East and we will all be safer.
Of course no mention of this during her Fox News interview.

I don't agree with the popular line that 9/11 was the result of a lack of democracy in the region, as much as it would be comforting to think that was the case. I think it was a lot more about the specificities of the Afghan Arabs and the support they received from Pakistan and Saudi Arabia.

My question: new security precautions aside, is another 9/11 more or less unthinkable after the invasion of Iraq?

I sincerely don't know.