"...the basic motivation of the war the terrorists feel themselves to have to fight."

The issues that radicalise people aren't necessarily the same as issues and the causes that they subsequently adopt. Once people have got sucked into identifying with a radical ideology, the human tendency is to take on board all kinds of other stuff.

I'm sure there were all kinds of ordinary Germans who got into supporting the Nazis because they were angry about being unemployed, or about political corruption or liked the pageantry and the strength through joy stuff. And went on from there to be drawn into other things.

So there is no contradiction between pointing to the war on Iraq as a crucial factor in driving many Muslims into the arms of the extremists, and recognising that the extremists have a wider agenda than Iraq. (In fact my conviction all along has been that while most Muslims - indeed most people outside of the USA - deplored the war, for the people at the heart of "Al Qaeda" it was something to be welcomed as an enormous success.)