LR35 FLT CREW LNDG PBI EXPERIENCED NMAC AT 3000 FT DURING VECTORS FOR VISUAL APCH TO RWY 27R.

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PBI APCH HAD US ON A LONG DOWNWIND TO RWY 27R. AT APPROX 25 DME; THE CTLR TURNED US TO A HDG OF 360 DEGS. AFTER THE HDG WAS ESTABLISHED; ATC ADVISED OF TFC (A BEECH JET) AT I BELIEVE HE SAID 10-11 O'CLOCK POS AND 4 MI; RPT TFC IN SIGHT. MY FO CALLED 'TFC IN SIGHT.' BUT I SAID NEGATIVE TO THE FO AND ALSO KEYED THE MIKE AND SAID NEGATIVE TO HAVING THE TFC IN SIGHT TO THE CTLR. SINCE MY LAST ASSIGNED HDG WAS 360 DEGS; I MAINTAINED IT. AFTER XING THE FINAL AND NOT HEARING ANY RESPONSE FROM THE CTLR; I STARTED TO CHALLENGE BUT HE TOLD ME TO MAKE AN IMMEDIATE TURN TO 180 DEGS. AT THAT TIME WE GOT A TA INDICATING AN NMAC. THE CTLR ASKED IF WE WERE CLRED FOR A VISUAL AND I REPLIED 'NO.' WE WERE BROUGHT BACK INTO THE FINAL AND WERE CLRED TO LAND. NOTHING ELSE WAS BROUGHT UP BY THE CTLR. SUPPLEMENTAL INFO FROM ACN 682890: ATC THEN SAID 'ACFT 10-11 O'CLOCK POS.' I ACKNOWLEDGED I SAW THE ACFT AND POINTED TO THE CAPT; BUT THE CAPT SAID NEGATIVE. HE TOOK THE RADIO AND TOLD ATC 'NEGATIVE ON TFC.' WE WERE STILL AT THE SAME 360 DEG HDG. ATC ASKED WHAT WAS OUR INTENTION. THE CAPT SAID 'WE ARE FOLLOWING 360 DEG HDG.' I WAS WATCHING TCAS AND THERE WAS TFC COMING TO OUR R SIDE; AND THE TCAS STARTED A TFC ALERT. THEN ATC GAVE THE DIRECTION TO IMMEDIATELY MAKE A L TURN TO HDG 180 DEGS.