SIMILAR A/N RESULT IN CLRNC TO DESCENT ACKNOWLEDGED BY WRONG ACFT.

Narrative

JAX CENTER CALLED OUR FLT NUMBER; 'COMPANY ABC DSCNT TO FL290.' WE WERE CRUISING AT FL330. I RESPONDED 'ROGER OUT OF 330 TO 290; COMPANY ABC.' THE CAPT WAS FLYING THE ACFT AND BEGAN TO DSND TO 29000'. I INFORMED THE CAPT THAT I WOULD BE OFF FREQ TO SET THE TPA ATIS. I WAS COPYING THE ATIS WHEN I FELT THE ACFT BEGIN TO LEVEL OFF; SO I LOOKED UP AND ASKED THE CAPT WHAT WAS THE MATTER? HE SAID THE CTLR QUESTIONED WHAT ALT WERE WE DSNDING TO. HE (CAPT) REPLIED THAT IT WAS TO OUR CLRED ALT OF FL290. THE CTLR TOLD HIM THAT THE CLRNC HAD BEEN GIVEN TO COMPANY ABD; NOT COMPANY ABC. AT THIS POINT COMPANY ABD WHO HAD NOT REPLIED TO COMPANY ABC CLRNC REPLIED THEY WERE LEVEL FL330. WE WERE THEN CLRED DOWN TO FL270 AND COMPANY ABD CLRED TO F290. THIS WAS GOING ON (THE CONVERSATION) AS I WAS ON THE OTHER FREQ. WHY DIDN'T THE CTLR CORRECT OUR REPLY TO HIS CLRNC WHEN WE REPLIED COMPANY ABC DOWN TO FL290? THIS WOULD HAVE AVERTED ANY ALT INFRINGEMENT OR MISCOM. THERE WAS NO EVASIVE ACTION NOR ANY OTHER TFC RPTED IN OUR AREA.