FOLLOWING A LATE RWY CHANGE; A B737-300 FLT CREW LANDED AT SLC WITH RVR BELOW LNDG MINIMUMS.

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PRIOR TO DEPARTING; SLC WAS REPORTING LOW VIS WITH FZ FG. WE WERE ASKED BY CD WHAT OUR LOWEST APPROACH CAT WAS BECAUSE THERE WAS A GATE HOLD UNLESS YOU WERE CAT III CAPABLE. WE DEPARTED AND WERE ASKED AGAIN BY CENTER WHAT OUR APPROACH CAT WAS. DESCENDING INTO SLC; WE GOT THE ATIS AND IT WAS REPORTING VIS OF 1 BR AND CLR SKIES. APPROACH ALSO ASKED US THREE TIMES WHAT OUR LOWEST WX CAT WAS. NOT REALLY KNOWING WHAT TO EXPECT; WE HAD BRIEFED CAT I; CAT II AND CAT III APPROACHES RWY 34L AND RWY 34R AT SLC. WHILE ON DOWNWIND; SLC APPROACH WAS CALLING OUT RVRS FOR BOTH RWYS; 34R WAS 6000; RWY 34L WAS 3000; 500; AND 500. THESE NUMBERS WERE FLUCTUATING WIDELY; AND APPROACH WAS GIVING UPDATES EVERY FEW MINUTES. WE DECIDED ON A CAT II APPROACH SINCE WE ONLY NEEDED 1200 RVR IN THE TDZ AND APPROACH HAD NOT BEEN CALLING THE MID RVR CONSISTENTLY ABOVE 700 FOR THE CAT III. APPROACH ADDED TO OUR WORKLOAD BY TELLING US TO PLAN FOR RWY 34L BUT SWITCH TO RWY 34R. WE ASKED FOR RWY 34R AND TOLD THEM THAT WE WANTED ONE RWY TO STICK WITH AND THEY TOLD US RWY 34L; WHICH HAD THE LOWER VISIBILITY OF THE TWO. TURNING TO INTERCEPT THE LOCALIZER AT APPROXIMATELY 18 DME; WE SAW THE AIRPORT; RWY 34L (ALL APPROACH AND RWY LIGHTS) AND RWY 34R. THE CAPTAIN TOOK CONTROL OF THE AIRCRAFT FOR THE CAT II APPROACH TO RWY 34L. BY THE TIME WE GOT TO THE FAF; I REMEMBER TOWER REPORTING THE TDZ AND MID RVR AS 500. WE HAD THE RWY IN SIGHT AND TOWER GAVE US CLEARANCE TO LAND. VISIBILITY WAS GOOD UNTIL WE TOUCHED DOWN AND THEN IT DROPPED IN THE FOG; BUT WE STILL HAD GOOD VISUAL REFERENCE ON THE RWY. WE ESTIMATED THAT THE FOG LAYER WAS ABOUT 20-30 FEET THICK. AFTER WE LANDED; WE WERE UNSURE IF WE WERE LEGAL TO HAVE CONTINUED PAST THE FAF WITH THE LOW RVR REPORTS EVEN THOUGH WE SAW THE COMPLETE RUNWAY ENVIRONMENT THROUGHOUT THE ENTIRE APPROACH. I GUESS MAYBE SOME CLARIFICATION FOR A SITUATION LIKE THIS. VISIBILITY IS THE ONLY REQUIREMENT TO FLY THE APPROACH. IS THAT AN ABSOLUTE? DOES THAT APPLY EVEN IF YOU CAN SEE THE RWY ENVIRONMENT FROM BEYOND THE FAF TO TOUCHDOWN?