The war in Iraq may actually be drawing terrorists away from other targets, as official US claims assert. But this does not necessarily mean that the neglected targets are in the Western. The real objective of Osama bin Laden and other Islamists is the overthrow of the Saudi regime, in order to secure control of the Moslem Holy Places in Mecca and Medina. This would provide the extremists with considerable legitimacy in the Moslem world.
The Saudi security forces had kept al Qaeda at bay up until 2003, when the American invasion of Iraq stirred up Islamic radicals world wide. While that led to al Qaeda attacks in Saudi Arabia, many more Saudi Islamic militants went off to Iraq, which was seen as the main battlefield. The Saudi government did little to halt this exodus, although it did pay attention to those who survived and returned. Most did not make it back, instead they were (usually) killed or (in a few cases) captured. This exodus gave the Saudi police a lot fewer terrorists to run down on their own turf. As a result, after two years, al Qaeda in Saudi Arabia was reduced to a small group of fugitives. Al Qaeda was still a dangerous force in Saudi Arabia, but not nearly as lethal as it might have been if so many of its most ardent supporters had not gone off and gotten themselves killed in Iraq.
Saudi Arabia was not the only Arab nation to benefit from the carnage in Iraq. An equal number of suicidal Islamic terrorists from other Middle Eastern nations also showed up, usually dead, in Iraq. Their governments back home were glad to see them go, although some of the families complained to the government in an effort to get their sons back. But since these trips were usually made illegally (by going to Syria, where an al Qaeda smuggling operation got them across the border), there was little the government could do except contact Iraqi officials and try to get the bodies back. Often there were only body parts, as many of these volunteers ended up as suicide bombers. American intelligence tried to identify as many of the suicide bombers as possible, including the use of DNA. The intel folks wanted to know where the bombers came from, and who they were. This allowed police back home to look into the dead man's friends and associates. That led to more al Qaeda getting arrested. Dead men do tell tales.