This photo looks like it’s been staged because I think if he gets shot, he should be falling down straight instead of butt facing the ground. However, I did change my mind after I read the article whereas O.D. Gllagher and Bill Mauldin both provided evidence to prove that Capa purposely staged the the photograph but later both of their evidence to be proven fake. Gllagher did not share a room with Capa and the photograph Maulin recognized was by George SIlk.
Also, I don’t think you would be able to have that much time to stage a photograph in battlefield. It was a period of war, if they wanted to stage a photo they did not have to go to a battlefield. They could have done it somewhere with a similar background, not having their life risked under flying bullets.
I think authenticity does matter, because when viewers are getting information from the photo they expected the information to be true and real. If the photo is fake, then what is the point of spending time to look at something that is unreal. But, sometimes a staged photograph is only meant to make the photo more convincing, it might have been staged but doesn’t mean it is not authentic.