"There’s no proof whatsoever that they originate in the tomb of Caiaphas,” he said. “It’s all conjecture."Even if we were sure that these nails came from the Caiaphas tomb, and even if we were sure that it is Caiaphas the High Priest's tomb, it is of course bonkers to assume that these nails would have been the nails from Jesus' crucifixion. But Barkay's comment makes clear that there is nonsense on top of nonsense here.
I took a look at the History Channel's schedules and noticed that they are broadcasting this documentary at 11pm, which hardly sounds like a ringing endorsement!