I'm not saying anything about the agressiveness of the AI, what I am saying is that after a successful crusade/jihad where the AI gets a province that is not near their other territory the AI seems to fall asleep.
I just had it happen again where Venice had a successful crusade to Jerusalem(i'm milan) now all their stacks do nothing even though I have left northern Italy very lightly defended. I've only seen 1 of their strategic pieces moving about. They have 3 full stacks around Ragusa doing nothing but I have noticed their ships moving about.