Wouldn't documentation of events lead to less dispute since it leaves fewer considerations for interpretation? Unless a photograph was alleged to have been staged, how would it lead to a dispute about the "narrative of the war"?

Putting that aside, one has to consider a few things. First, the general public did not have a great deal of exposure to battlefield photographs until Matthew Brady's Antietam exhibit in October 1862. Soldiers would not have had much exposure to these photographs (outside of newspaper reporting of it), for the papers they got usually had wood-cutting pictorials, not pictures. What exposure these soldiers did have to photography largely came via the studios that advertised services more akin to the "senior photo" nowadays. In other words, soldiers may have paid to have their picture taken in camp, or while on furlough, so that they could send it to a loved one, yet as it concerns battlefield photography, they would likely not have seen much of it. These exhibits largely took place in places like New York, so a battlefield soldier wouldn't have been terribly aware of it.

Second, photographers largely photographed the after-effects of a battle, once the armies had mostly moved on. So again, soldiers wouldn't have been very aware of this process, as they would have likely been en route somewhere else by the time the photographers started getting their shots. Even if the soldiers were still nearby, they would have been more interested in getting their own photo taken than with the morbid work of seeing their dead friends getting immortalized for all time.

[Source: Bruce Catton, 'Grant Moves South' & 'Grant Takes Command']