The liar's dividend is only half the story. Once any recording can be waved away as synthetic, the cost falls on whoever cannot afford to prove otherwise.
You had to accuse someone of forgery. You needed a theory of who made it and how, and the how was expensive: equipment, a technician, hours of somebody's skilled time. You had to say it out loud, in front of people who would remember that you said it, and if the photograph turned out to be genuine your accusation became the second piece of evidence against you. None of that proved the photograph. It only meant that denying it was not free. That price, and not any property of light on film, is what the authority of a photograph always consisted of.