If they are indeed running at night, I would hope they have something more than that letter as authorization. That letter was rescinded almost immediately with the FCC citing problems with the computer program used to recalculate PSA's and PSSA's. And even if it were a legitmate authorization, please note that the August power level is 1 watt.
The FCC "lost" all of the records of old PSAs on the old regional channels. If you have the old Western Union telegram you can still use PSA. If your station does not have that telegram you are "stuck" with flea or no power. Maybe they did not get the letter that it was rescinded. Could they run some kind of part 15 scheme. I have never heard of part 15 on AM except for some roadside warnings the D.O.T. put up on roadside construction.