NOTING AN APPARENT PAX SEAT BACK PROBLEM; OFF DUTY FAA INSPECTOR REQUESTS FLT ATTENDANT OF MD80 IN CRUISE TO SHOW HER THE FLT ATTENDANT MANUAL. FLT ATTENDANT NOTIFIES CAPT; WHO DENIES REQUEST DUE SECURITY CONCERNS WHEN ADVISED FAA INSPECTOR HAS NOT SHOWN HER CREDENTIALS. AFTER LNDG; CAPT VERIFIES INSPECTOR ID; AND OFFERS TO PROVIDE MANUAL; BUT INSPECTOR ADVISES SHE WILL CHECK THE FAA COPY AT HER OFFICE.

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DURING CRUISE; FLT ATTENDANT INFORMED US THAT A PAX INFORMED HER THAT SHE WAS WITH THE FAA OFF DUTY AND WOULD LIKE TO LOOK AT HER MANUAL. SHE ASKED ME IF SHE SHOULD SHOW IT TO HER AND I ASKED IF THE PAX HAD SHOWN HER HER CREDENTIALS. FLT ATTENDANT #1 SAID THAT SHE HAD NOT; SO I TOLD HER NOT TO SHOW HER FLT ATTENDANT MANUAL BECAUSE OF SECURITY CONCERNS. I WAS LATER INFORMED THAT THE ALLEGED FAA INSPECTOR WANTED TO KNOW THEIR PROCS FOR HANDLING A SEAT BACK THAT WOULD NOT STAY UPRIGHT FOR TKOF. APPARENTLY SEAT XB SEAT BACK WOULD NOT STAY UPRIGHT DURING TAXI OUT; AND ONE OF THE FLT ATTENDANTS WORKED THE CTL AND SHOOK THE SEAT BACK WHICH APPEARED TO FIX THE PROB. I WROTE UP THE SEAT AND HAD THE FLT ATTENDANT TELL THE ALLEGED FAA INSPECTOR THAT I WOULD BE HAPPY TO TALK TO HER ON THE GND. AFTER GATE ARR I DID TALK TO THE FAA INSPECTOR AND OFFERED TO LET HER LOOK AT A FLT ATTENDANT MANUAL NOW THAT I OBSERVED HER FAA CREDENTIALS. SHE DECLINED; SAYING THAT SHE COULD CHK THE FAA'S COPY OF THE MANUAL AT HER OFFICE; AND THAT SHE WOULD BE LOOKING INTO AIRLINE'S PROCS; AND POSSIBLE DESIGN FLAWS IN OUR PAX SEATS.