ZLA CTLR GIVES WRONG FLT AN AMENDED CLRNC ALT CHANGE. POTENTIAL CONFLICT LTSS WITH ACFT 2 MI ABEAM.

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IN CRUISE; APCHING ONT; LEVEL AT FL350; REQUESTED LOWER ALT FROM ZLA. CTR CAME BACK AND CLRED US TO FL240. AS WE STARTED DOWN; I CALLED 'CALL SIGN; LEAVING FL350 FOR FL240.' NO RESPONSE; SO EVERYTHING WAS OK. AFTER DSNDING APPROX 1000-1500 FT; CTR TOLD US TO MAINTAIN FL350. AS THE FO CLBED BACK UP; I QUERIED CTR ABOUT WHY. HE SAID CLRNC WAS FOR A 'COMPANY' ACFT. THE FO AND I BOTH DISTINCTLY HEARD THE CLRNC FOR US TO DSND TO FL240. (THE SO WAS ON ANOTHER RADIO.) ON THE GND; I TALKED TO THE CREW OF THE OTHER COMPANY ACFT AND THEY ALSO HEARD OUR CLRNC TO FL240. AFTER CLBING BACK UP TO FL350; CTR GAVE US TFC AT 2 O'CLOCK; 2 MI AT FL330. WE WERE THEN GIVEN A FREQ CHANGE WITH NO FURTHER EXPLANATION. IF WE HAD TCASII; WE WOULD NEVER HAVE STARTED DOWN IF THE ABOVE TFC WAS A CONFLICT. THE FAA SHOULD REQUIRE TCASII ON ALL LARGE ACFT; NOT JUST PAX ACFT. I BELIEVE THE CTLR THOUGHT HE WAS TALKING TO THE OTHER ACFT (THEY WERE AT FL280 DURING THIS OCCURRENCE); AND CONFUSED THE CALL SIGN. SUPPLEMENTAL INFO FROM ACN 361455: THE PNF CAPT READ BACK THE CLRNC IN FULL. OUR DSCNT CLRNC READBACK WAS NEVER QUESTIONED BY CTR. WE BELIEVE THAT THE CTLR MADE AN ERROR. OUR COMPANY ACFT AHEAD HAD A VERY SIMILAR FLT NUMBER.