That's not quite correct. The event was real, and several of the men in it died later in the fighting on Iwo Jima. What it is not is a photo of the first flag raising on Mt. Suribachi. A smaller flag was raised first, but it could not be easily seen from the beaches or elsewhere on the Island. Thus the second larger flag was ordered to be raised. There was also a thing about the Secretary of the Navy wanting the original flag as a souvenir, but before that could happen, the order to replace the flag, and secure the original for the battalion, was issued.
I've read that when the first flag was raised, it was early in the attack on the island. Once they had cleared the top of that mountain, the soliders were ordered to go put a flag on the top of that mountain. When they did, there was still many japanese with artilary within firing range, and they went absolutely nuts when they saw the american flag go up. The moutain started getting pounded by the Japanese from every direction.
It was later, once the area was more secure and the top of the mountain was out of enemy firing range, that the second flag raising took place with film cameras rolling. I saw a pretty detailed account of this on the history channel.
I don't think the fact that the more famous of the pictures is the second raising. It doesn't take away at all what happened. Only idiots would consider it "controversial" since their is visual evidence of both flag raisings. Those that do have an agenda to bash and they can go take a long walk off a short pier.