According to Szarkowski, the difference between the thing that is shown in a photograph or the subject of the photograph is reality itself. He states that the photograph deals with the actual and him as a photographer would accept it and “treasure” it. The problem was that as a photographer, one would have to see the invisible picture rather than the reality brought forth. The photograph might be more important than the thing itself because it captures the truth. Viewing the thing itself with the naked eye is more of “an illusion” states Szarkowski. The image would be the only thing keeping the thing alive and becomes the “remembered reality”.
In your third sentence, Szarkowski means something a little different than I understand you to mean. He states that the photographer has to choose to make a visually engaging image-make the invisible picture visible-over accurately capturing reality. In so doing, the photographer also conveys a particular viewpoint about the thing shown.