WHILE ON SHORT FINAL TO SJC ARPT; AN ACR PIC SPOTS TFC ON A BASE LEG TO A PARALLEL RWY APPEARING TO BE OVERSHOOTING AND CONVERGING ON THE AIRLINER.

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AFTER BEING SWITCHED TO SJC TWR WHILE CONDUCTING A VISUAL APCH TO RWY 30L; THE LCL CTLR ISSUED TFC AT 11 O'CLOCK POS; 3 MI ON L BASE TO RWY 29. I WAS THE PNF AND RESPONDED TO THIS ADVISORY WITH A 'ROGER' AS WE DID NOT HAVE THIS VFR TFC IN SIGHT. WHEN I DID FINALLY SIGHT THIS TFC; WE WERE ON ABOUT A 1 1/2 MI FINAL TO RWY 30L AT APPROX 450-500 FT AGL. THE VFR TFC WAS ON A L BASE TO RWY 29 APCHING OUR FLT PATH ON A 90 DEG ANGLE ON A DIRECT COLLISION COURSE ABOUT 1 MI AWAY AT 11 O'CLOCK POS. I WATCHED THIS TFC TO MAKE SURE HE TURNED FINAL TO RWY 29 AND WHEN HE APPEARED TO PASS THROUGH THE RWY 29 EXTENDED CTRLINE; I BECAME VERY CONCERNED AND ASKED ATC 'IS THIS GUY GOING TO TURN FINAL?' THEY RESPONDED BY TELLING THE TFC TO START A TURN TO FINAL UPON WHICH THE PLT ENTERED AN IMMEDIATE VERY STEEP TURN TO THE L WHICH TOOK HIM OFF THE DIRECT COLLISION COURSE THAT HE WAS ON WITH OUR ACFT. HAD THIS PLT NOT TURNED WHEN HE DID WE WOULD HAVE EXECUTED A GAR TO PREVENT CONTINUED LOSS OF SEPARATION. ONCE IT WAS CLR THE ACFT WAS NO LONGER A THREAT; I COMMENTED TO THE LCL CTLR; 'I DON'T MIND TELLING YOU THAT WAS VERY DISCONCERTING.' CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED INCIDENT WAS VERY CLOSE TO BEING AN NMAC. CTLR AT SJC SEEMED UPSET THAT THERE WAS SO MUCH CONCERN WITH FLC ABOUT THE INCIDENT. CTLR TOLD THE CAPT IT WAS A SEE AND AVOID PRINCIPLE; AND HE DIDN'T UNDERSTAND WHAT THE PROB WAS.