B737 CREW HAD AN NMAC WITH A LIGHT ACFT AFTER THE TWR CTLR CLRED THE LIGHT ACFT TO LAND ON A PARALLEL RWY. THE B737 CREW WAS UNABLE TO ESTABLISH VISUAL CONTACT WITH THE LIGHT ACFT AHEAD; AT PIE.

Narrative

WHILE ON A VISUAL APCH (FIRST MISTAKE) USING LOC BC RWY 35R AT KPIE WITH FO FLYING; TWR ADVISED US THAT LIGHT ACFT WOULD BE LNDG SIMULTANEOUSLY ON THE PARALLEL RWY 35L. I ACKNOWLEDGED THIS INFO AND SHORTLY (VERY!) TWR POINTED OUT TFC FOR THE PARALLEL. NEARLY SIMULTANEOUSLY; TCASII GENERATED A TA; FOLLOWED BRIEFLY BY A DSND RA. I HAD MY TCASII AT A MINIMUM 5 MI SETTING AND THE RA TARGET APPEARED CO-LOCATED ON THE DISPLAY. THE RA INSTRUCTED 'DSND;' WHICH I FOUND UNUSUAL THAT CLOSE TO THE GND. WE FRANTICALLY SEARCHED FOR THE TFC AND ELECTED TO GO AROUND. IT SEEMED LIKE THERE WAS NO PLACE TO GO FOR TFC THAT COULD NOT BE SEEN AND I FEEL THAT THE FO'S STRAIGHT AHEAD MISSED APCH WAS PROBABLY AS SAFE AS ANY DECISION. SURPRISINGLY ENOUGH; THE TWR CTLR SOUNDED PISSED OFF AT US FOR GOING AROUND INSTEAD OF CONTINUING TO LAND. NOT BEING ABLE TO SEE SOMEONE WHO SHOULD HAVE BEEN AT APPROX 10-11 O'CLOCK POS AND WELL LESS THAN 1 MI. MYSELF; THE FO; AND THE JUMPSEATER ALL AGREED (LATER) THAT WE ALL IMAGINED THE LIGHT ACFT HAD LINED UP FOR THE WRONG RWY. THE ONLY OTHER MANEUVER AVAILABLE MAY HAVE BEEN A R BREAK; BUT THE STRAIGHT AHEAD 'GO' WORKED. I TOLD THE CTLR WE WERE 'RESPONDING TO AN RA' AND THEN; 'ON THE GO; RESPONDING TO AN RA.' THE CTLR'S RESPONSE WAS (SOMETHING LIKE) 'I TOLD YOU HE WAS THERE...' EITHER THE CTLR DIDN'T UNDERSTAND 'RA' OR HE HADN'T LEARNED THE LESSON TAUGHT BY THE B757 MIDAIR WITH THE RUSSIAN ACFT IN EUROPE RECENTLY. WE LIVED TO FLY ANOTHER DAY.