Iraqis believe that their Arab neighbors are using Iraq as a way to get rid of their Islamic radicals. Syria, in particular, does little to stop Islamic radicals from entering Iraq. The Syrians know that most of these men will get killed. Those that survive and return, can be arrested, questioned to see if they are still willing to die to establish an Islamic state, and release them if they have mellowed out. Saudi Arabia and the other Arab Gulf States are accused of doing the same thing. These countries remember what happened during the 1980s, when eager young men went off to fight for Islam in Afghanistan, and the survivors came back eager to start an Islamic revolution in their home countries.
Actually, very few of the Arabs who went to Afghanistan got killed there. The Afghans were reluctant to take, into combat, inexperienced Arab volunteers who didn't even speak the local languages. But the Arab volunteers, like Osama bin Laden, stayed in Pakistan working with Afghan refugees and helping out as they could. Then these fellows went home full of enthusiasm for establishing Islamic republics. This resulted in the formation of Islamic rebellions in many Arab countries. In Iraq, many of the volunteers, even though they speak the local language (although with an accent that gives away their foreign origin), were also shunned by the more experienced Sunni Arab gunmen leading the fight against the government and coalition forces. Many of the foreigners are used as suicide bombers, as all this requires is driving a few miles, then pushing a button.
The Arab volunteers, in effect, identify themselves as Islamic radicals by going to Iraq. Frequently, even their families are surprised when they discover a son has gone off to Iraq. This is often considered a tragedy, because if the kid doesn't get killed in Iraq, he will be on a police list of usual suspects when he comes back.
It's thought that several hundred foreign volunteers died in Fallujah, a city that many volunteers headed for when they entered Iraq. Fallujah was the center of suicide bomb operations, and an area where foreign volunteers were prepared for suicide missions, or given training to make them useful as gunmen or for planting roadside bombs. But many of these volunteers never left Fallujah, as it was easier to use locals (who knew the neighborhood) to plant roadside bombs, or make attacks on local police. So when the battle for Fallujah happened, many foreign volunteers for a chance to fight. They were pretty inept, and many of those who got caught by bombs, and didn't leave behind enough information to identify nationality, were believed to be foreign Arabs. Interrogations of over a thousand captured gunmen in Fallujah indicated that lots of foreigners were there, and had been encouraged to stay there and fight. Most apparently did, and died. Only a few dozen were captured.
Iraqis are angry with their neighbors for allowing these bloodthirsty men to come to Iraq to kill people. Most of the casualties inflicted by the foreign Arabs are Iraqi. The government is increasingly vocal in demanding that their neighbors crack down on these "volunteers," but little is actually being done. Getting rid of your local Islamic radicals is too good an opportunity to pass up.