Well, my memory is fading somewhat but from my classes in "History and Traditions of the Marine Corps" at MCRD in 1965 comes this version.
One of the platoon commanders in the company that had been assigned to take Suribachi had placed a small American flag inside his jacket in case the opportunity presented itself. When they took the summit, they placed it on a piece of pipe and raised it. A Marine combat photographer captured that raising on film. The brass on the command ship wanted a larger flag that could be seen from everywhere on the island so a larger flag was sent in along with a group of civilian journalist. Joe Rosenthal (sp??) was one of them. They accompanied the Marines to the top of Mt. Suribachi to get a better vantage point of the fighting on the island. In a later interview, Rosenthal was asked if the photo was staged and he said "No, as a matter of fact, I almost missed it." It seems that he was looking in another direction and one of the other journalist said "Hey, look at that." Rosenthal said that as the flag was being raised he turned and quickly took the shot. At that time, film was sent back to a rear area to be processed and cleared by the censors before being released. He said that he had pretty much forgotten about it. Sometime later when the film was processed, one of the developers saw it and remarked "Wow, look at this." The next day that picture appeared in almost every newpaper in the country with the caption "MARINES CAPTURE MT. SURIBACHI".
The rest is history.
Semper Fi