For what Szarkowski wanted to point out was that photos show a different side to an event compared to what a person sees with their own eyes. The photographer’s job is to try and make the photograph as believable as possible within it’s limitations. A photograph is a still image, so it might not accurately portray the action in motion correctly. Photos are also confined to the frame of the image (or being limited to what it can see) which there might be more of the image that the camera is not picking up. This makes the image seem more focused onto certain objects. A photo can also manipulate what the end result of the image is, either through a controlled environment or editing after the fact. Lastly, the subject of the photograph can be open to interpretation and can be different than what the subject is portrayed in real life.
The reason photographs are more important because more people will see the photo than the one who have experienced the event first hand. Since the real world is always in a constant motion, it hard to make something believable without hard evidence. With a photograph (and to an extent, video and audio) capture a moment in that constant motion that would last longer than the people involved with it. There is also the sense that a photograph is given more care to what it sees than a person seeing that same event as it happens.