How could they tell there were imaginary flashes? It seems like a private experiment, you can't check it. (Maybe there were not expected flashes at all and they saw some anyway?)
According to the book, after using the counter to confirm that properly trained and rested humans were as accurate as the electronics, the next step was to put the electronic counter away because the humans could also give you spatial information: They could not only tell you that a flash had happened, but could tell you where it was in the visual field. Multichannel PMTs or (god bless 'em) chilled semiconductor-based multi-element low-noise photodetectors were still dozens of years in the future...