B737 CREW ON APCH INTO OAK IS GIVEN TFC OPPOSITE DIRECTION DECLINED A TURN TO THE R BY THE CTLR AND TURNED L IN REACTION TO A TCASII RA ALERT TO CLB.

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APCHING OAK FROM THE SE (APPROX 130 DEGS/20 MI); APCH CALLED TFC AT 12 O'CLOCK POS. INITIALLY NOT SEEN ON TCASII; BUT DID SHOW WITHIN 3-5 SECONDS THEREAFTER APPROX 4 MI AHEAD AND SAY 500 FT LOW. ALTHOUGH CLRED TO 7000 FT; WE STOPPED THE DSCNT AND LEVELED AT 8000 FT. TFC APPEARED STILL LOW AND PRESENTED ON THE TCASII AT ABOUT 1-2 O'CLOCK POS. ALTHOUGH I'M NOT SURE OF THE SEQUENCE WITHIN THE NEXT FEW SECONDS; ALL OF THE FOLLOWING OCCURRED: 1) APCH DIRECTS A R TURN TO 340 DEGS; 2) AS THE CAPT (PM); I CALLED 'NEGATIVE R TURN; WE'RE COMING L;' 3) TCASII RA TO CLB; 4) VISUAL ON TFC AT ABOUT 12:30-1 O'CLOCK LOW. THESE ITEMS ALL OCCURRED IN THE SPACE OF 10-15 SECONDS. EASILY CLRED TFC PASSING ABOVE; AND THE OTHER ACFT (I THINK A COMANCHE LIGHT ACFT) CALLED A VISUAL AND PASSED BELOW. APCH THEN ASKED WHY WE DISREGARDED HIS GUIDANCE AND I EXPLAINED THAT OUR TCASII PRESENTATION INDICATED THAT A R TURN TO THE DIRECTED 340 DEG HDG WOULD HAVE PUT THE TFC AT OUR DEAD 12 O'CLOCK POS. I THEN ASKED FOR A PHONE NUMBER AND STATED THAT I WOULD BE HAPPY TO CALL ON THE GND TO DISCUSS THE OCCURRENCE. WHEN I CALLED THE NUMBER; I DISCUSSED THE INCIDENT WITH THE SUPVR. HE HAD APPARENTLY LISTENED TO THE TAPE AND TOLD ME THAT HE HAD NO PLANS TO 'TAKE THE ISSUE FURTHER.' SUPPLEMENTAL INFO FROM ACN 616678: THE CAPT AND I SEARCHED VISUALLY AND VERIFIED THE TCASII; BUT SAW NO TFC EITHER OUTSIDE OR ON THE TCASII. WE STILL COULD NOT FIND HIM VISUALLY SO; I ELECTED TO LEVEL THE ACFT OFF AT 8000 FT. WE ADVISED THE CTLR WE MADE A 20 DEG L TURN TO AVOID THE TFC. HE ASKED IF TCASII GAVE US HORIZ INSTRUCTIONS AS WELL. WE SAID NO; ADVISED HIM WE MADE THE TURN TO AVOID THE RA AND THE FACT THAT THE ACFT STARTED CLBING UP ON US.