The experiment could simply be measuring photon counts at a pre-agreed location after a pre-agreed duration, where the elapsed time is measured by a local clock. (Probably it is reasonable to argue that this is not a "reasonable" experiment, but it's beyond me to make rigorous the sense in which it should be excluded.)

For example, someone could never logically claim the photons they perceived indicted someone wasn't in front of their gun when they pulled the trigger, while everyone else in the vicinity states they clearly saw the person in front of the gun. There is not enough uncertainty around the behavior of photons for us to consider their explanation as truth.