It's not accidental. Every single time someone asks him about the reasons for invading Iraq, he starts off talking about 9/11 and al-Qaeda. He never directly says Iraq was involved, but he always groups the two together. It's actually a pretty nifty propaganda technique; he never directly associates them, rather, he mentions them in the same breath and lets people make the association for themselves. This way he can stand back and say "I never said Iraq was involved in 9/11," while still making the association every time he talks about it.
One time, he actually said that he was "careful" to not say that Iraq was responsible for 9/11.
IOW, he knows he is pushing the limit and has to tip-toe to make sure that he doesn't go over the line.
OTOH, he has never been careful to not link the attack of Iraq with 9/11. He does that all the time, including when he answered her question.
Just listen to his answer. What was the real reason to attack Iraq? Terrorists, Taliban, Afghanastan, 9/11. And "I thought Iraq was a threat." Which had nothing to do with 9/11 terrorists, the Taliban, or Afghanastan, but it was important to mention it anyway.
The stupid thing is, there IS an answer to her question, that does not require such obfuscation. He could have said,
The events on 9/11 taught us that we can't sit back and be passive in defending ourselves, and we had to be more aggressive in being preemptive. We thought Iraq posed a significant enough risk to our security that it was important to depose them before they had the opportunity and wherewithall to attack us.
Now, there are aspects in there that are debatable, particularly the part about Iraq posing a significant enough risk to our security, and are they the only ones that do, but that is a question of where we draw the line, not whether it should be drawn (and I don't think the part about having to be more aggressive in being preemptive is all that debatable). Yet, there is no mention of the Taliban or 9/11.
I think that would have been a perfectly acceptable answer to her question. I don't agree with it, but then again, I don't have access to all the information the president had, so it makes it really hard to dispute at that point. Most importantly, unlike the answer he gave, it is not one giant non-sequitor.