In fact, as this New York Times op-chart makes clear, the truth is just the opposite. White and Hispanic soliders are overrepresented among military personnel killed in Iraq, whereas African American soldiers are underrepresented. (Blacks account for 18.6 percent of military personnel in Iraq, but account for only 10.9 percent of military personnel killed.)
The same was true in World War II, the Korean War, and the 1991 Gulf War. In Vietnam, sometimes referred to as a war fought by black men against yellow men on behalf of white men, blacks accounted for 12.5 percent of all combat deaths versus 13.1 percent of the young male adult population of fighting age.
Not that those who have been spreading this myth will let the facts get in the way, but there you have it.
(Thanks to reader Bob Wray for bringing the Times op-chart to my attention.)