If the Marines seem in a hurry, it's not because they were play acting; they were under enemy fire.
James Bradley's book Flags of our Fathers includes an excellent description of the whole event. unfortunately, the movie of the same name was virtually all fiction.
You are absolutely correct - it was not a setup and it’s a disservice to Rosenthal and the marines as well, to say so.
And, I will add, Flags of Our Fathers is a fantastic book. I just read Flyboys by Bradley last month. Very good but not as good as FOOF.