B737-200 LANDS WHEN THE RPTED WX IS BELOW MINIMUMS.

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UPON FIRST CONTACT WITH FSD APCH WE WERE ADVISED RPTED WX AS 7 OVCST 1 SM SN FZDZ. RWY 3 LOC OTS. WIND 010 DEGS AT 12 KTS. WE INFORMED APCH WE NEEDED ONE AND ONE QUARTER MI VISIBILITY FOR THE APCH AND REQUESTED HOLDING. WE HAD ONLY APPROX 10 MINS HOLD FUEL. ONCE IN THE HOLD; A NEW CTLR CAME ON FREQ TO INFORM US THE WX IS STILL SHOWING 1 MI VISIBILITY. HOWEVER; TWR VISIBILITY IN THE REMARKS SECTION OF THE SEQUENCE SAYS ONE AND ONE QUARTER MI. WE 'CAN'T GET THE WX BUREAU TO CHANGE THEIR OBSERVATION; SO THE OFFICIAL VISIBILITY IS 1 MI.' BEFORE I COULD COMMENT THE CAPT TOLD APCH WE COULD ACCEPT THE APCH. WHILE BEING VECTORED TO THE VOR-DME RWY 33 AT FSD; I CHALLENGED THE DECISION AND TOLD THE CAPT WE'RE NOT LEGAL FOR THIS APCH; OFFICIALLY THE VISIBILITY IS 1 MI. THE CAPT USING VERY POOR 'CLR' CONTINUED THE APCH. I DID ALL MY DUTIES TO ENSURE A SAFE CONCLUSION. AFTER ARRIVING AT THE GATE AT FSD; I REFED THE SECTION IN THE OPS MANUAL UNDER PREVAILING VISIBILITY AND SHOWED HIM MY POS. HIS INTERP OF THE PARAGRAPH LED HIM TO BELIEVE HE WAS LEGAL. I STILL DO NOT BELIEVE WE WERE LEGAL TO SHOOT THE APCH. I AM STILL INVESTIGATING. THE CAPT USED POOR 'CLR.' UPON REALIZING HALF THE CREW DIDN'T AGREE WITH HIS COURSE OF ACTION; HE SHOULD HAVE RECONSIDERED HIS ACTION AND ERRED ON THE CONSERVATIVE SIDE.