THE ATCT LCL CTLR ISSUED RWY VISIBILITY AS ONE QUARTER MI; WHEN HE SHOULD HAVE ISSUED RVR. THE CREW HAD TKOF MINIMUMS AT ONE QUARTER MI AND DID NOT WHEN 1100 FT RVR WAS ISSUED.

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WE WERE TAXIING OUT AT RSW AT XA534 TO RWY 6. THE TWR WAS STILL CLOSED BUT THE WX RPTED WAS 1/4 MI FOG. ONCE WE REACHED RWY 6; THE TWR OPENED. WE OBTAINED OUR CLRNC TO MIA AND WERE CLRED FOR TKOF. BUT ATC CALLED THE WX RVR 800 FT. WE DECLINED TKOF (RWY TKOF MINIMUMS 1600 FT RVR OR 1.4 MI) AND ADVISED TWR WE NEEDED 1600 FT RVR. WE LATER SHUTDOWN 1 ENG AND ADVISED TWR TO GIVE US A HEADS UP WHEN THE VISIBILITY WOULD COME UP TO START AN ENG. WHEN THE VISIBILITY CAME UP TO 1100 RVR; TWR GAVE US A CALL TO START #1 ENG. THE TWR THEN RPTED 1/4 MI VISIBILITY. WE THEN ADVISED TWR WE COULD ACCEPT TKOF CLRNC. AS WE WERE TAKING OFF; THE TWR QUESTIONED WHY NOBODY HAD TAKEN OFF WHEN HE HAD RPTED 1/4 MI ALL MORNING. DURING DISCUSSIONS BTWN RSW TWR AND OTHER ACFT ON THE GND; WE HEARD THE TWR SAY 'RVR 1100 FT; VISIBILITY 1/4 MI.' IF HE HAD GIVEN US THIS INFO BEFORE TKOF; WE WOULD HAVE DECLINED TKOF CLRNC. WE FELT THE TWR WAS CONTRADICTING AND CONFUSING. WE ALSO FEEL WE SHOULD HAVE BEEN PROACTIVE AND QUESTIONED THE RVR AND NOT ASSUMED THE WX HAD IMPROVED TO SUCH THAT THE TWR WAS NO LONGER USING RVR'S. SUPPLEMENTAL INFO FROM ACN 576013: WE OBTAINED AN ENRTE CLRNC AND WERE CLRED FOR TKOF WITH A NEWLY RPTED 800 FT RVR. SINCE THIS WAS LESS THAN THE 1600 FT RVR REQUIRED (IF VISIBILITY WAS RPTED AS RVR); WE DECLINED THE TKOF AND WAITED FOR VISIBILITY TO IMPROVE. SUBSEQUENT RPTS FROM ATC WERE 700 FT RVR; 1200 FT RVR AND TEN 1/4 SM FOG; RESPECTIVELY. AN ACR FLT IN LINE BEHIND US ADVISED ATC THEY WOULD NOW BE ABLE TO DEPART.