Time says this:
Eastwood's portrayal of the specific battle is, if narrow, also essentially accurate. Flags Of Our Fathers zeroes in on the soldiers who hoisted the U.S. flag atop Mount Suribachi, and this task, memorialized in a famous staged photograph, was accomplished by five white servicemen and a sixth, Ira Hayes, of Pima Indian descent. (His other entry in the Iwo Jima category, Letters from Iwo Jima, is told largely from the perspective of Japanese soldiers.)
Joe Rosenthal's famous photo wasn't staged. It was the second raising of the flag but Rosenthal got the second shot because commanders wanted to keep the first flag for the battalion instead of handing it over to the US Secretary of the Navy, James Forrestal.