RWY INCURSION AT MEM; TN; WHEN XING CLRNC READBACK IS NOT QUESTIONED BY TWR WHO PURPORTS THAT IT WAS NOT GIVEN.

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APCHING INTXN OF TXWYS A AND C I BROUGHT THE ACFT TO A STOP. OUR CLRNC WAS HOLD SHORT OF RWY 27 AT TXWY C. GND CTL WAS CONFUSED AS TO WHERE WE WERE AND ASKED US IF WE WERE THE ACFT ON TXWY N. THE FO REPLIED; NO; ACR X IS ON TXWY A. A DC10; WAS TRYING TO CLR RWY 27 AT THE END AND THERE WAS A B727 APCHING THE INTXN OF TXWYS A AND N (A CONFLICT). GND CTL'S XMISSIONS APPEARED TO BE SOMEWHAT BROKEN OR INCOMPLETE. WHILE RECEIVING OUR COMPANY'S RAMP PARKING CONFIRMATION FROM THE RAMP TWR; GND CTL CALLED - THE FO (ALL OF US AGREED) BELIEVED WE WERE 'CLRED ACROSS RWY 27 ON TXWY C.' HE READ BACK THE CLRNC AS 'ACR X CLRED TO CROSS RWY 27 ON TXWY C.' THE DC10 WAS STILL CLRING THE RWY TO OUR L AND THE CLOSEST ACFT VISIBLE ON FINAL WAS 5-6 MI OUT. I TURNED ON THE TAXI LIGHT; RELEASED BRAKES; TURNED L ONTO TXWY C; VISUALLY CLRED BOTH DIRECTIONS AGAIN THEN CROSSED RWY 27 AT TXWY C. N OF RWY 27 AS WE WERE TURNING E ON TXWY V; GND CTL ASKED 'ACR X; IS THAT YOU N OF RWY 27?' THE FO ANSWERED 'ACR X AFFIRMATIVE. YOU CLRED US ACROSS.' THE GND CTLR STATED 'NO; I DID NOT.' THE REMAINING TAXI TO PARKING WAS UNEVENTFUL. I TALKED TO THE TWR SUPVR LATER (ABOUT 30 MINS LATER). HE SAID WE WERE NOT CLRED TO CROSS BUT CONFIRMED OUR READBACK; GND CTLR'S FAILURE TO CATCH IT AND BAD RADIO RECEPTION AS WELL AS 'CONFUSION.' NO FURTHER ACTION.