This was in the days when there were no electronic cameras and everything was mechanical. So, basically Rosenthal's shot was a happy accident.
Rosenthal later took a staged shot when the flag had been raised with most of the Marines at the summit that he called his "gung ho" shot because of the poses the men took.
There was no dark room on Iwo so Rosenthal dropped his film into a pouch to Guam. He had no idea what he had captured. As soon as the photo came out of the dark room, Guam knew what they had and radioed the photo back to America where it was on the front page of darn near every paper.
Lowery claimed the photo had to have been staged, perhaps out of jealousy. Somebody asked Rosenthal if the photo had been staged and thinking they were talking about the gung ho photo said it was. He immediately corrected himself, but the rumor persists to this day.
These are interesting tidbits of history but the power of the photo, as you say, is that it embodies the fundamental spirit of the Marine Corps and the way they fought the worst battle in the history of the Corps.
The Rosenthal shot was sent to the states via what we now call fax, but darn it was slow back then.
The Lowery shots and more:
http://www.cnn.com/2015/02/22/world/cnnphotos-iwo-jima/
I think this is Lowery’s obit:
http://articles.latimes.com/1987-04-18/local/me-887_1_iwo-jima
Never heard that Lowery claimed Rosenthal’s photo was staged. Another version says the accusation began with Time magazine (what a surprise). Someone from the publication asked Rosenthal if the photo was staged; thinking they were referring to the “gung ho” photo (taken after the second flag-raising), the AP photographer replied “yes.” It took him several weeks to get Time to correct their reporting.
Incidentally, Lowery’s photos of the first flag raising didn’t appear in Leatherneck until 1947.