Everyone, everywhere, at all times should fight against the U.S.
Should some unranked Iraqi soldier have fought against the U.S., or followed the orders of his commanding officers (who, by the way, probably received a literal briefcase full of cash or gold from a CIA operative) to stand down?
Not assassinating leadership is a long-standing rule/tradition of war. Hell, in most of historic European war-making, knights would wade through the ranks of common soldiers slaughtering without mercy, but could generally expect to be captured for a ransom rather than being killed themselves (it was far more than just their armor which protected them).
It's nice to be able to treat war like a game, and not have it put your own life at much risk. Turns the meat grinder into a nice, tidy little chess board you can place friendly little bets over.