The photographer is a guy named John Moore who has been all over the place photographing combat.
The story is here in The Guardian.
IMO, in that account, he doesn't resolve whether or not it was proper for him to take that picture.
It's a tricky question.
I usually trend toward taking a photo (provided the right lens allows you to not disturb), then considering if its proper to run it. I suppose each part has different risks.
There's a line I thought was interesting from a great story in Esquire, where it explains the experience of photographer pictures of Bobby Kennedy's death.
"The photographer is no stranger to history; he knows it is something that happens later. In the actual moment history is made, it is usually made in terror and confusion, and so it is up to people like him—paid witnesses—to have the presence of mind to attend to its manufacture. The photographer has that presence of mind and has had it since he was a young man. When he was twenty-one years old, he was standing right behind Bobby Kennedy when Bobby Kennedy was shot in the head. His jacket was spattered with Kennedy's blood, but he jumped on a table and shot pictures of Kennedy's open and ebbing eyes, and then of Ethel Kennedy crouching over her husband and begging photographers—begging him—not to take pictures.
Richard Drew has never done that. Although he has preserved the jacket patterned with Kennedy's blood, he has never not taken a picture, never averted his eye. He works for the Associated Press. He is a journalist. It is not up to him to reject the images that fill his frame, because one never knows when history is made until one makes it."
In the case of the Arlington photo, I often wonder about names. Is it better to have one because the memory of the person lost burns stronger? Is it worse, because the person in it becomes an object of interest? All somewhat unanswerable.