That isn't true according to the law. According to the law, the following entities can be wiretapped without a warrant (provided the AG determines no American's are not involved which is the delay the article refers to but after reading the law it appears to be add'l issues)
(a)
“Foreign power” means—And according to section 1802, the following must require an advance court ruling(1) a foreign government or any component thereof, whether or not recognized by the United States;
(2) a faction of a foreign nation or nations, not substantially composed of United States persons;
(3) an entity that is openly acknowledged by a foreign government or governments to be directed and controlled by such foreign government or governments;
(4) a group engaged in international terrorism or activities in preparation therefor;
(5) a foreign-based political organization, not substantially composed of United States persons; or
(6) an entity that is directed and controlled by a foreign government or governments.
http://www4.law.cornell.edu/uscode/50/usc_sup_01_50_10_36_20_I.html
That's only true within the United States. Outside the United States (and Iraq is certainly not in the US) NSA powers are much broader. If the Iraqis in question were within the US, I can see the NSA having had to work to get a FISA warrant. But that's not the situation here.