DURING PREFLT INSPECTION OF AN ACR; FLC WERE CHALLENGED BY FAA INSPECTOR AS TO THE PROC USED TO VERIFY FUEL QUANTITY OF A FUEL TANK IN WHICH THE GAUGE WAS INOP AND DEFERRED. THE INSPECTOR'S QUESTIONS WERE SUBSEQUENTLY SATISFIED AND THE FLT CONTINUED TO PREPARE FOR DEP; EVEN THOUGH THE INSPECTORS DELAYED THE FLT.

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ARRIVING AT ACFT; FO AND I NOTED THAT MAINT WAS ATTEMPTING TO CORRECT AN INOP L MAIN FUEL GAUGE. SHORTLY THEREAFTER MAINT STATED THAT THEY WOULD BE DEFERRING THIS ITEM AS PER MEL. WE WERE THEN MET BY FAA INSPECTORS AND ANOTHER INSPECTOR. THEY ASKED TO INSPECT OUR LICENSES; MEDICAL AND MY CONTACT LENSES; SINCE I HAVE A RESTR FOR CORRECTIVE LENSES ON MY MEDICAL. THE INSPECTION OF OUR LICENSES AND MY MANUALS WAS NORMAL AND IN ORDER. HOWEVER; THE INSPECTION OF FO'S ACFT OPERATING MANUAL REVEALED THE LATEST REVISION WAS NOT ENTERED. FO EXPLAINED TO ONE OF THE INSPECTORS THAT HE WAS IN THE PROCESS OF ADDING THIS REVISION BUT WAS PRESENTLY WORKING ON ANOTHER MATTER; IE; THE INOP FUEL GAUGE MEL. FO ADDED THAT THE REVISION WOULD BE COMPLETED PRIOR TO OUR DEP. INSPECTOR THEN BEGAN A SERIES OF QUESTIONS REGARDING THE MEL. THIS ADDED TO THE DELAY OF OUR FLT. INSPECTOR QUESTIONED HOW I WOULD HANDLE THE INOP FUEL GAUGE. I RESPONDED THAT I WOULD REFER TO OUR MEL BOOK AND FOLLOW THE PROC. HE EXPLAINED THAT HE WAS NOT SATISFIED WITH MY RESPONSE AND REQUESTED FURTHER EXPLANATION. I STATED THAT I WOULD BE USING THE 'DRIPLESS METHOD' TO VERIFY FUEL QUANTITY AND/OR MAKING SURE OF A KNOWN FUEL QUANTITY. HE APPEARED DISSATISFIED WITH MY RESPONSE AND ADDED THAT I SHOULD NOT TRUST A MECH OR FUELER TO VERIFY THE FUEL LOAD AND HE RECALLED AN ACFT ACCIDENT WHICH OCCURRED AS A RESULT OF A SIGNIFICANT FUEL IMBALANCE. ADDITIONALLY INSPECTOR SAID I SHOULD BE OBSERVING THE ENTIRE FUELING PROCESS. AFTER REFERRING TO THE MEL BOOK I PROCEEDED TO DIP THE L MAIN TANK WITH A MECH. BOTH THE MECH AND MYSELF DIPPED THE TANKS AND READ THE INCLINOMETERS INDEPENDENTLY AND COMPARED OUR FINDINGS. DURING THIS PROCESS INSPECTOR FOLLOWED MY EVERY STEP INCLUDING ATTEMPTING TO ENTER THE NOSEWHEEL WELL WITH ME WHILE I WAS READING THE INCLINOMETERS. I PROCEEDED TO THE ACFT AND VERIFIED OUR FUEL LOAD USING THE DATA COLLECTED; AND THE FUELING MANUAL. I INSISTED TO OUR MECH THAT I WANTED TO VERIFY THE AMOUNT OF FUEL ADDED TO THE L MAIN TANK. THE FUELER ARRIVED AND STATED THE AMOUNT OF FUEL THAT WAS ADDED TO THE EMPTY L MAIN TANK. THIS AMOUNT CONCURRED WITH OUR ORIGINAL QUANTITY OBTAINED FROM THE DRIPLESS METHOD. I THEN APCHED BOTH INSPECTORS AND ASKED IF THERE WAS ANYTHING ELSE THEY NEEDED TO SEE OR DID NOT FIND ACCEPTABLE; TO WHICH THEY REPLIED NO. SINCE THERE WAS TENSION AND A SOMEWHAT ADVERSARIAL RELATIONSHIP DURING OUR INSPECTION; I REITERATED THAT IT WAS MY INTENTION TO OPERATE THE ACFT TO THE HIGHEST DEGREE OF SAFETY AND THAT IF THEY OBSERVED SOMETHING ABNORMAL I WOULD APPRECIATE THEIR INPUT. THEY REPLIED THAT EVERYTHING WAS FINE AND THEY HAD NOTHING FURTHER.