FLC OF AN MLG OVERSHOT DSCNT ALT DUE TO ATC NOT HEARING THE INCORRECT READBACK ALT BY THE FLC.

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CAPT WAS OFF ATC FREQ TALKING WITH COMPANY. FO TOOK ATC CLRNC TO DSND TO 13000 FT AT 40 DME. AT APPROX 14500 FT ATC ASKED IF WE WERE AT 16000 FT (THE ALT ATC ALLEGES WE WERE CLRED). ON EXAMINING ATC TAPES SUBSEQUENT TO EVENT; IT WAS DISCOVERED THAT OUR CREW (FO) DID READ BACK A DSCNT TO 13000 FT; WHICH IS THE NORMAL ALT FOR LNDG DIRECTION AT THE ATC 041 DEG RADIAL; 40 DME. WE CONTINUED DSCNT TO 13000 FT AND CALLED 'CTR' ON GND. ZTL INDICATED THAT THE TAPE OF THE OCCURRENCE INDICATED OUR READBACK OF 13000 FT WHICH THEY INDICATED THEY DID NOT CATCH. WE JOINED THE ARR AS A FAST MOVER (330 KTS) FROM THE LOW ALT SECTOR 22000 FT. SOME DIFFICULTY MIGHT HAVE OCCURRED FOR THE ATC CTLR AS HE WAS TRYING TO WORK US INTO THE ARR ALONG WITH THE HIGH ALT ARRS. THEY (ATC) INDICATED THE LOSS OF SEPARATION OCCURRED WITH AN INBOUND ACFT AT 15000 FT. HAD BOTH PLTS BEEN ON FREQ; A BACKUP FOR THE ALLEGED 16000 FT CLRNC WITH A SUBSEQUENT 13000 FT READBACK MIGHT HAVE BEEN AVOIDED. AT NO TIME DID WE RECEIVE A TCASII ALERT WITH THE 15000 FT TFC.