I think the math is very interesting from a forensics point of view. My guess is that since the NYT photographer took the photo it would be hard to assign a motive for him altering the photo, either something in your math is missing or more likely as you noted the photographer was wrong about speed he was shooting or perhaps the camera was not operating at the speed it was intended to...

My experience is that most of the time the most likely answer is the right one. In this case, your math suggests for some reason the camera was operating at 1/4000th shutter speed.

To be clear, I am not disparaging you and I do think the agencies handling the investigation have been less than forthcoming with what they know.