B777; SFO ARR; AT FL380 EXPERIENCED CONFLICT WITH PRECEDING TFC AT FL390 WHEN ATC ERRED AND ISSUED DESCENT TO FL390 ACFT; OPERROR RECORDED.

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WE WERE 10 NM W OF CREAN; INBOUND TO SFO AT FL380. ACR Y WAS APPROX 5 NM AHEAD OF US; AT FL390. WE HAD BOTH BEEN GIVEN A SQUAWK. ACR Y HAD BEEN CALLED IN RADAR CONTACT A COUPLE OF MINS EARLIER. WE WERE BOTH TALKING TO ZOA. THE RIDE BEGAN TO GET CHOPPY AND BOTH ACR Y AND OURSELVES ASKED FOR LOWER ALT. WE WERE BOTH VERY CLOSE TO TOP OF DSCNT POS. OAK HEARD BOTH OUR REQUESTS AND RESPONDED; 'ACR Y DSND AND MAINTAIN FL350.' HE READ BACK THE CLRNC. OUR POS WAS APPROX 5 NM BEHIND HIM; AND 2 NM OFFSET TO THE R OF HIS TRACK TO CREAN. WHEN THE CTLR SAW ACR Y IN A DSCNT HE ASKED; 'ACR Y SAY CLRED ALT.' ACR Y RESPONDED WITH FL350. THE CTLR GAVE US A 30 DEG R TURN AND INSTRUCTED ACR Y TO MAINTAIN ALT. WE TURNED AND TOLD THE CTLR THAT WE CONCURRED WITH ACR Y THAT THE DSCNT CLRNC WAS FOR HIM; NOT US; AND HE HAD READ IT BACK. I BELIEVE THE CTLR MOMENTARILY GOT CONFUSED WITH BOTH OF US ASKING FOR LOWER; AND GAVE THE DSCNT CLRNC TO ACR Y INSTEAD OF US. NEITHER OF US ASKED HIM TO ACKNOWLEDGE THE MISTAKE; BUT I'M QUITE SURE THAT IS WHAT HAPPENED. NO TCAS ALERT WENT OFF; AND WE WERE VFR AND IN SIGHT OF ACR Y.