Clearly untrue. Perhaps it is easier for you to view an enemy as a lunatic monster bent on senseless destruction, but nearly every mass murdering organization in the world, whether it's a terrorist group like Al Qaeda or a military power like the US, has very concrete motivations and objectives for its actions, and is well versed in the logic of power. Realpolitik is deeply rooted in a rational worldview. You may disagree with the premises or the reasoning (I certainly do), but calling Al Qaeda 'completely irrational' is way off.
But how will the bottom- and middle-tier guys they know they're taking orders from Bin Laden's designated successor and not agents of some country's (you name it) intelligence services?
It takes a nontrivial amount of planning, preparation, money, and coordination to pull off the kind of simultaneous suicide operation we saw in Sept 2001.
It goes:
People get pissed off > They band together and share their anger > They decide to do something about it > They do something about it.
After the fact WE brand them as part of a large effective organization, 01/09/11 did require funding and planning due to the requirement to fly planes and the synchronization of multiple TEAMS.
The Madrid and London rail bombings required almost none (find people, make explosives, pick time/place, synchronize watches).
The activities in Iraq require almost no planning and really demonstrate that there is no globe spanning plan, if there was all the Iraqi suicide bombers would travel somewhere US interests can be attacked more easily. But they don't, ergo 'AQ' is actually a loose collection of people with similar motivation and very limited ability to communicate or distribute funds globally.