B767 FLC HAS TCASII ALERT DURING APCH TO SFO.

Narrative

WE WERE CLRED TO ARCHI INTXN AT 7000 FT TO PLAN FOR THE FMS BRIDGE VISUAL RWY 28R. THIS APCH WAS BRIEFED AND INSERTED INTO THE FMS. PRIOR TO REACHING ARCHI ASSIGNED BY ATC A HDG OF 220 DEGS AT 210 KTS AND TO PLAN FOR AND TO INTERCEPT FOR THE VISUAL RWY 28L. MY FO CONFIGURED THE FMS AND WE BRIEFED FOR THE APCH. ATC THEN CHANGED OUR CLRNC AGAIN FOR US TO PROCEED DIRECT TO ARCHI INTXN AND CLRED US FOR THE FMS BRIDGE VISUAL RWY 28R AGAIN. BY THE TIME THE FO HAD SET UP ARCHI IN THE FMS; WE WERE PRACTICALLY OVER THE INTXN; MAYBE INSIDE. SINCE THE INSTRUCTION FROM ATC WAS CLRED FOR THE FMS VISUAL AND WE WERE INSIDE ARCHI; I INSTRUCTED MY FO TO SET 6000 FT ON THE MCP AND STARTED DSCNT SO AS TO CROSS NEXT FIX 'TRDOW' AT OR ABOVE 6000 FT. THROUGH APPROX 6700 FT; WE RECEIVED A TCASII RA 'TFC ALERT.' I RESPONDED BY FOLLOWING RA AND CLBED TO 7000-7200 FT. ATC SHORTLY AFTER CAME ON AND TOLD US TO MAINTAIN 7000 FT AND GAVE US A HDG RIGHT OFF COURSE TO 280-285 DEGS AND THEN RECLRED US FOR THE FMS RWY 28R AFTER WE INFORMED HIM THAT WE HAD THE RWY IN SIGHT. REST OF APCH WAS UNEVENTFUL. WX WAS A FACTOR; AS WAS ATC/PLT WORKLOAD. WE WERE GETTING TASK SATURATED DUE TO THE CHANGES IN CLRNCS OVER A SHORT PERIOD. ALSO; CONFUSION AROSE WHETHER THE CTLR ACTUALLY WANTED US TO DSND AS WE DID FOLLOWING THE FMS BRIDGE VISUAL RWY 28R. I WAS QUITE CERTAIN HE CLRED US FOR THE APCH.