I think you've got that right.
I see this as a paralell to WWII. With Iran as Germany and Syria as Italy.
Iraq, to me, is like the Spanish Civil war (or Algeria, someone else pointed out -- altho now I'm going to have to go research that).
If you have Netflix or a similar service, rent The Battle Of Algiers and watch that. Shows both sides very fairly and honestly. Not only is it a classic and insightful look into a Western counterinsurgency effort against an Islmic uprising, including a look at torture as an interrogation techique, bombing civilians with IEDs, the media effect on the war, and other eerily similar issues, but it has a large cult following.
In al-Qa'ida.
It was Abu Musab al-Zarqawi's favorite movie, and versions of the movie are found among pretty much any AQ hideout or training camp that's hit. The AQ versions generally have a few scenes edited out, involving women doing un Islamic things like putting on makeup. Still, it's a classic among jihadist circles, and it's well worth our attention, too.