ALT DEV ACR X DSCNT TO WRONG ALT THROUGH OCCUPIED ALT OF ACR Y.

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BNA APCH GAVE ACR X A HDG AND A DSCNT TO AN ALT WE UNDERSTOOD TO BE 5000 FT MSL. APCH CTL ADVISED AN ACR Y OF OUR POS AND ASSIGNED ALT; WHICH THE CTLR SAID WAS 8000 FT MSL. WE HEARD THIS ON THE RADIO AND BROKE INTO SAY 'NEGATIVE; WE'RE CLRED TO 5000 FT MSL.' THERE WAS NO CONFLICT AND APCH CTL DID NOT ALTER OUR COURSE AND ALT INTO BNA. (WHEN THE APCH CTLR TOLD THE COMMUTER WE WERE ASSIGNED 8000 FT MSL. WE WERE APPROX 6000 FT MSL DSNDING TO 5000 FT MSL.) SUPPLEMENTAL INFO FROM ACN 299434: PLT ASKED APCH WHAT ALT THE X JET (I ASSUMED TO BE US) WAS DSNDING TO. APCH SAID 8000 FT TO WHICH I IMMEDIATELY RESPONDED WE WERE CLRED TO 5000 FT; THE ALT IN OUR REMINDER WINDOW. APCH ASKED THE PLT IF HE COULD MAINTAIN VISUAL SEPARATION ON US AND HE SAID YES. AT THIS TIME I NOTICED THAT ONE OF THE SEVERAL TARGETS ON OUR TCASII SCREEN WAS 2-3 MI BEHIND AND 200 FT ABOVE US. I ASSUME THIS WAS THE FLT AT 6000 FT AND THAT WE MUST HAVE DSNDED THROUGH HIS ALT IN FRONT OF HIM. WE NEVER GOT ANY TCASII ADVISORIES NOR RECEIVED ANY HDG OR ALT CHANGES FROM APCH DURING THIS TIME AND BOTH ACFT CONTINUED TO BNA AND LANDED. AFTER ARR I CALLED APCH ON THE PHONE AND EXPLAINED THAT TO THE BEST OF OUR KNOWLEDGE WE BELIEVED OUR CLRNC WAS TO 5000 FT NOT 8000 FT. I WAS TOLD 'THERE'S NOT GOING TO BE A PROB AS LONG AS YOU DON'T CHANGE YOUR STORY' WHICH I DIDN'T UNDERSTAND.