A300 CREW LNDG MEM START DSCNT TO INTERIM ALT AND LEARN FROM CTLR THAT THE CLRNC WAS FOR ANOTHER ACFT WITH A SIMILAR CALL SIGN. LATER; THE PLT BELIEVES THE CTLR CAUSED AN NMAC.

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ON VFR ARR INTO MEM AND CLRED DIRECT TO THE MCGHE FIX; ZME ARR APCH CTLR CLRED OUR ACFT (ACR XX) TO DSND TO 6000 FT FROM 10000 FT. AFTER A SHORT 2-3 SECOND DELAY TO MAKE SURE NO ONE ELSE RESPONDED; MY FO (AS PNF) ACKNOWLEDGED THE CLRNC. THERE WAS NO REPLY NOR CONFIRMATION FROM THE APCH CTLR. WHEN PASSING THROUGH 9700 FT; THE CTLR QUERIED US AS TO WHAT ALT WE WERE CLRED TO MAINTAIN. OUR RESPONSE WAS '6000 FT.' HE IMMEDIATELY SHOT BACK THAT THE LAST ALT CLRNC WAS FOR ACR YXX; NOT ACR XX. AFTER A VERY SHORT CONSULTATION/DISCUSSION WITH MY FO; THE FO REPLIED WE HAD READ BACK THE CLRNC AS STATED AND FURTHER; THAT THE CTLR HAD OFFERED NO CORRECTION TO OUR REPLY NOR HAD HE EVEN QUESTIONED OUR RESPONSE. THE CTLR THEN ALLOWED US TO CONTINUE OUR DSCNT TO 6000 FT. MOMENTS LATER IN THE ARR; THE CTLR KEPT OUR ALT FIXED AT 5000 FT UNTIL ABOUT 15 MI FROM THE FIELD; AT WHICH POINT HE CLRED US FOR A VISUAL APCH TO RWY 36R. I WAS UNABLE TO DSND IN PROPER MANNER ACCORDING TO ESTABLISHED COMPANY PROCS TO FULLY ESTABLISH A STABILIZED APCH BY 500 FT AGL AND; BY COMPANY REG; WAS REQUIRED TO INITIATE A MANDATORY GAR. UPON CHK-IN WITH THE SAME APCH CTLR ON THE GAR PHASE; HE POSITIONED OUR FLT ON A BASE TURN TO RWY 36L FINAL IN DIRECT AIR-TO-AIR CONFLICT WITH A COMPANY ACR Z ACFT APPROX 4 MI AT OUR 12 O'CLOCK POS; AND TOLD US TO FLY A VISUAL TO RWY 36L. WE INFORMED HIM WE DID NOT HAVE THE RWY IN SIGHT; ALL THE WHILE CONTINUING TO CONVERGE ON THE 12 O'CLOCK TFC. AT APPROX 2 MI SEPARATION; I VISUALLY ACQUIRED THE END OF RWY 36L AND COMPLETED A VISUAL APCH TO A FULL-STOP LNDG.