ACR WDB CLRNC RESPONSE TO WRONG CALL SIGN CAUSES WRONG RWY APCH INTO MEM.

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WE WERE TOLD TO CHANGE ILS APCH FROM 36L TO 36R; WHICH WE ACKNOWLEDGED; RETUNED AND PROCEEDED WITH THE INTERCEPT OF RWY 36R ILS. WHILE OUTSIDE ELVIS (OM) WE WERE TOLD BY APCH THAT IT APPEARED THAT WE WERE ON ILS 36R COURSE AND NOT 36L COURSE. WE ACKNOWLEDGED THAT WE WERE CHANGED FROM RWY 36L TO 36R ILS WHILE BEING VECTORED FOR THE INTERCEPT. CTLR SAID NEGATIVE; REINTERCEPT ILS 36L AND CLRED TWR AT MARKER FOR 36L. THE CLRNC FOR ILS 36R WAS FOR ANOTHER ACFT. I ACKNOWLEDGED NEW CLRNC FOR RWY 36L AND LNDG WAS UNEVENTFUL. ALL 3 COCKPIT CREW MEMBERS HEARD THE CLRNC TO CHANGE TO ILS 36R WHILE BEING VECTORED. I CALLED APCH CTL AFTER LNDG TO GET A TAPE REVIEW. THE CTLR CALLED LATER AND TOLD ME THE SEQUENCE HE SAID THEY READ FROM THE TAPES. IT APPEARS ACCORDING TO WHAT THE CTLR TOLD ME VIA TELEPHONE; THAT I ACKNOWLEDGED A CLRNC FOR ANOTHER ACFT AND THAT THE CTLR DID NOT CATCH THE CALL SIGN OF US ACKNOWLEDGING THE WRONG CLRNC. I WISH 2 MISTAKES WOULD MAKE 1 RIGHT; BUT LUCKILY TFC WAS LIGHT AND NO SEP STANDARDS WERE BROKEN ON THE APCH (ACCORDING TO APCH SUPVR). ALL 3 COCKPIT CREW MEMBERS WOULD SWEAR ON A BIBLE THAT WE HEARD THE RECLRNC TO ILS 36R DURING OUR VECTORS FOR APCH; WHICH I ACKNOWLEDGED DELIBERATELY AND WITH OUR CALL SIGN. I CAN'T BELIEVE THIS HAPPENED BECAUSE BOTH ACFT HAD TO BE INITIALLY VECTORED FOR ILS 36L. THE CTLR THEN WANTED 1 OF 2 ACFT TO CHANGE FROM ILS 36L TO ILS 36R. WE ACKNOWLEDGED THE RECLRNC AND WE DID NOT HEAR AN ACKNOWLEDGEMENT FROM THE OTHER ACFT. NOW HE SHOULD HAVE BEEN GOING TO RWY 36L AND WE SHOULD HAVE BEEN GOING TO RWY 36R. WE BOTH ENDED UP ON ILS'S TO RWY 36R. WE BELIEVE THAT WE WERE NOT HEARING PHANTOM VOICES AND THAT CTLR SCREWED UP. MURPHY'S LAW!