A B737-300 CREW WAS GIVEN CLRNC TO DSND TO AN OCCUPIED ALT IN A80 CLASS B AIRSPACE.

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ACR FLT ORIGINATED IN ZZZ AND TERMINATED IN ATL. THE CAPT WAS THE PF. ZTL GAVE US A DSCNT TO 14000 FT MSL AND SWITCHED US TO ATL APCH CTL. WE CHKED IN WITH APCH; ADVISING THEM WE WERE DSNDING TO 14000 FT WITH THE CURRENT ATIS INFO. ON THE REPLY BY APCH; A DSCNT CLRNC TO 10000 FT WAS GIVEN BUT THE CALL SIGN WAS NOT CLR. TO ENSURE IT WAS OUR CLRNC; I ASKED THE CTLR TO CONFIRM HE WANTED ACR XYZ TO DSND TO 10000 FT. HE REPLIED AFFIRMATIVE. WHILE LEVELING AT 10000 FT; THE APCH CTLR QUERIED OUR ALT. WE REPLIED WE WERE LEVELING AT 10000 FT. HE IMMEDIATELY TOLD US WE HAD CONFLICTING; CO-ALT TFC AT 12 O'CLOCK POS AND DIRECTED US TO CLB IMMEDIATELY TO 11000 FT. HE STATED WE SHOULD HAVE BEEN AT 12000 FT. HE CONTINUED POINTING OUT THE TFC AND TELLING US TO CLB. WE COMPLIED. PASSING THROUGH 10500 FT; THE CAPT IDENTED THE TFC. NEITHER THE CAPT NOR I HEARD ANY TCASII WARNING. ONCE CLR OF THE CONFLICTING TFC; WE WERE SWITCHED TO ANOTHER APCH CTL FREQ AND CONTINUED TO ATLANTA. THE APPARENT CAUSE OF THIS POTENTIAL CONFLICT WAS THE ISSUANCE AND CONFIRMATION OF A DSCNT TO 10000 FT BY ATC FOR ACR XYZ. IN THE FUTURE; WHEN A CREW ASKS FOR A CLRNC CONFIRMATION; EXTRA CARE IS WARRANTED TO ENSURE A CLRNC IS CORRECTLY COMMUNICATED AND RECEIVED.