If I'm reading him correctly, Jaynes is arguing that while reports of ESP are evidence for ESP, they're even stronger evidence that the reports are somehow mistaken.

I don't have my copy of PT:LOS right here, but this doesn't sound right to me. I would think that your prior probability for the reports being mistaken is greater than your prior for ESP. The reports provide strong evidence for a mistake, and even stronger evidence for ESP, but not strong enough to make ESP look more probable than a mistake.