CORP ACFT HAS NMAC WITH METROLINER WHEN FO SIGHTS WRONG TFC FOR VISUAL SEPARATION.

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WE DEPARTED ORANGE COUNTY/JOHN WAYNE ARPT (SNA); DEST: SUN VALLEY; ID (SUN). OUR DEP CLRNC HAD US ON RADAR VECTORS TO INTERCEPT THE SXC 084 DEG RADIAL TO SXC THEN DIRECT LAX; FLT PLAN RTE. SHORTLY AFTER CLRING THE NEWPORT BEACH; CA; SHORELINE; WE WERE GIVEN A HDG OF 210 DEGS AND AN ASSIGNED ALT OF 8000 FT. THE CTLR ADVISED US OF TFC (METROLINER) AT A POS OF 1-2 O'CLOCK RELATIVE TO OUR ACFT. SHORTLY THEREAFTER; MY FO RPTED TFC WHICH HE BELIEVED TO BE THE TFC POINTED OUT BY ATC. ATC THEN ISSUED US A CLB CLRNC TO 10000 FT; BUT INSTRUCTED US TO MAINTAIN VISUAL SEPARATION FROM THE RPTED TFC. I NEVER SAW THIS RPTED TFC AND QUERIED MY FO AS TO WHERE THE TFC WAS BEFORE I INITIATED A CLB. MY FO TOLD ME 'THE TFC' WAS PASSING OPPOSITE DIRECTION OFF THE R SIDE OF OUR ACFT AND WOULD BE NO FACTOR TO OUR FLT PATH. THINKING WE WERE CLR OF OUR TFC; I BEGAN THE CLB TO 10000 FT; ON A HDG OF 210 DEGS. DURING THE CLB I NOTICED ANOTHER 'METROLINER' ACFT PASSING L TO R AND BELOW US. I ALSO BECAME AWARE THAT THE SUN WAS LOW AND BRIGHT; WHICH WAS CAUSING A SLIGHT DISTR. WHILE IN THIS CLB MY ATTN WAS ALSO FOCUSED INSIDE THE COCKPIT; AT MY HSI BECAUSE MY HDG CLRNC OF 210 DEGS WAS TO INTERCEPT THE SXC 084 DEG RADIAL TO SXC. THIS RADIAL WAS SOON TO BE 'ALIVE.' THE CTLR THEN TOLD US; 'WE COULD PROCEED DIRECT TO SXC IF WE LIKE;' MAKING NO FURTHER MENTION OF CONFLICTING TFC. I CTRED THE CDI NEEDLE AND TURNED DIRECT TO SXC WITH THE USE OF THE 'HDG MODE' ON OUR AUTOPLT. WE WERE APCHING 9000 FT IN OUR CLB TO 10000 FT. I THEN REFOCUSED MY ATTN OUTSIDE THE COCKPIT WHERE I NOTICED TFC AT OUR 1-2 O'CLOCK POS. AT FIRST I THOUGHT IT TO BE A LARGE 'B747' TYPE OF ACFT LOCATED MUCH FARTHER AWAY. CONTINUING TO OBSERVE THIS TFC; I SOON REALIZED IT WAS MUCH CLOSER TO US THAN PREVIOUSLY THOUGHT AND THAT THIS TFC WAS CLOSING IN ON OUR INTENDED FLT PATH FROM OPPOSITE DIRECTION AND TO OUR R. I DISENGAGED AUTOPLT AND TIGHTENED MY R TURN; BUT THE CLOSURE RATE AS WELL AS MY DELAYED REACTION TO THE TFC HAD BROUGHT OUR 2 ACFT EXTREMELY CLOSE TO ONE ANOTHER. THE PLT OF THE OTHER ACFT; METROLINER; CAME ON FREQ (128.10); OBVIOUSLY UPSET AND SAID TO THE CTLR; 'I THOUGHT YOU SAID THAT ACFT HAD US IN SIGHT!' I THEN REALIZED THIS WAS THE TFC WE WERE SUPPOSED TO HAVE RPTED IN SIGHT AND TO HAVE MAINTAINED VISUAL SEPARATION FROM. WE CONTINUED THE REST OF OUR FLT (UNEVENTFUL) TO OUR DEST; SUN; WHERE I CONTACTED SOCAL TRACON VIA TELEPHONE TO EXPLAIN WHAT HAD HAPPENED. INCIDENTALLY; THE PLT OF THE OTHER ACFT FILED A 'NMAC RPT.' HUMAN PERFORMANCE CONSIDERATIONS: ALTHOUGH THERE WERE NUMEROUS ACFT FLYING IN OUR VICINITY; THE FO MAY HAVE BEEN HASTY IN RPTING THE APPROPRIATE TFC IN SIGHT. PER COMPANY POLICY HE ALSO SHOULD NOT RPT AN ACFT OR ARPT IN SIGHT UNTIL BOTH PLTS (HE AND I) HAVE VISUAL CONTACT. HAVING BELIEVED MY FO AND THAT WE WERE CLR OF OUR RPTED TFC; I HAD ERRONEOUSLY BELIEVED THAT I HAD A CLR PATH IN OUR CLB FROM 8000 FT TO 10000 FT. BECAUSE OF THIS I DIVERTED SOME OF MY ATTN FROM OUTSIDE TO INSIDE THE COCKPIT. AFTER HEARING A CLRNC FROM ATC WHICH SAID; 'I COULD PROCEED DIRECT TO SXC IF I'D LIKE TO;' WITH NO FURTHER MENTION TO OUR TFC; I HAD NO REASON TO BELIEVE WE HAD A TFC CONFLICT. THE CONFLICTING TFC WAS INITIALLY HIDDEN FROM OUR SIGHT DUE TO THE BRIGHT; LOWERING SUN. WE THEREFORE COULDN'T SEE WHAT WE WERE SUPPOSED TO AVOID. WHILE OPERATING ON AN INST FLT PLAN; OUR COMPANY WILL NO LONGER ACCEPT A CLRNC WHICH REQUIRES US TO REMAIN CLR OF CERTAIN ACFT OR OBSTACLES UNLESS BOTH PLTS HAVE A POSITIVE IDENT. ALTHOUGH WE MUCH APPRECIATE THE HELP OF ATC TO EXPEDITE OUR CLBS TO MORE FUEL-EFFICIENT ALTS; I WOULD RECOMMEND THIS TYPE OF CLRNC (MAINTAIN VISUAL SEPARATION) NOT BE GIVEN WHILE IN A BUSY TERMINAL AREA; ESPECIALLY WHEN IT CAN BE SEEN THAT THE FLT PATHS OF THE 2 ACFT WILL BE IN CLOSE PROX TO ONE ANOTHER. ALTHOUGH IT IS THE ULTIMATE RESPONSIBILITY OF THE PIC TO 'SEE AND AVOID;' I THINK THE CTLR COULD HAVE BEEN MORE ASSERTIVE IN AGAIN POINTING OUT OUR CONFLICTING TFC ONCE IT WAS SEEN THATOUR FLT PATHS WOULD BE COMING AS CLOSE TOGETHER AS THEY DID. SINCE THERE WERE NUMEROUS ACFT SIGHTED IN OUR VICINITY; IT MIGHT HAVE ALSO BEEN HELPFUL IF ATC HAD POINTED THEM OUT TO DIFFERENTIATE THEM FROM THE ONE THEY HAD INTENDED US TO AVOID.