B727 CREW CROSSED RWY IN ZZZ WITHOUT CLRNC.

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ON NOV/WED/00; I WAS THE FO ON A B727 ON A SCHEDULED FLT FROM ZZA TO ZZZ. AFTER LNDG AT ZZZ; WHILE TAXIING TO THE PARKING AREA; WE WERE EBOUND ON TXWY S OF RWY. AS WE APCHED TXWY WE UNDERSTOOD THE GND CTLR TO SAY; 'ACR XYZ; CROSS RWY ON TXWY.' I READ BACK; 'UNDERSTOOD; ACR XYZ IS CLRED ACROSS RWY ON TXWY.' THE GND CTLR DID NOT RESPOND AS HE WAS VERY BUSY. WE VISUALLY CHKED FOR CONFLICTING TFC AND SEEING NONE; PROCEEDED ACROSS RWY. UPON REACHING THE N SIDE OF THE RWY; THE GND CTLR ASKED IF OUR ACFT WAS ON THE N SIDE OF THE RWY. I RESPONDED 'YES; WE UNDERSTOOD HE HAD CLRED US TO CROSS RWY ON TXWY.' HE REPLIED HE HAD NOT. UPON REVIEWING THE VOICE RECORDINGS; POS OF THE RECORDING WERE BLOCKED OR UNINTELLIGIBLE. NO OTHER ACFT WERE ON THE RWY AT THE TIME AND NO EVASIVE ACTIONS OR GAR'S WERE REQUIRED. IN MY OPINION; SAFETY WAS NOT COMPROMISED OTHER THAN THE MISUNDERSTANDINGS IN COM. I BELIEVE THIS SIT OCCURRED AS A RESULT OF 'BLIND SPOTS' IN THE VHF COM COVERAGE ON GND AT ZZZ; THE TEMPO OF OPS AND THOSE INVOLVED THINKING THEY HEARD WHAT THEY WERE EXPECTING TO HEAR. FURTHER OCCURRENCES CAN BE PREVENTED BY DOUBLECHKING CLRNCS WHEN COMS ARE POOR; INCOMPLETE; OR UNCLR. SUPPLEMENTAL INFO FROM ACN 492365: ON NOV/WEB/00; AT APPROX XA35; WE WERE TAXIING TO THE RAMP AFTER LNDG AT ZZZ. I (SO) WAS DOING THE AFTER LNDG SILENT CHKLIST AND THOUGHT I HEARD GND CTL CLR US TO CROSS RWY AT TXWY. THE FO READ BACK THE CLRNC TO CROSS. WE CHKED FOR TFC; WHICH THERE WAS NONE; AND PROCEEDED ACROSS RWY. ONCE WE WERE ACROSS THE RWY AND TURNING ONTO TXWY; THE GND CTLR QUERIED IF WE WERE ON THE N SIDE OF THE RWY. THE FO REPLIED; YES HE HAD JUST CLRED US; TO WHICH HE REPLIED; NO HE HAD NOT. WE TAXIED IN TO PARKING; SHUT DOWN; AND WENT IN TO OPS TO DEBRIEF. THE CAPT NOTIFIED THE SUPVR AND CALLED THE TWR SUPVR. WE WERE OVER AND MET WITH THE TWR SUPVR AND LISTENED TO THE TAPE; WHICH SOUNDED A BIT CLIPPED. WE HEARD 'ACR XYZ HOLD SHORT OF RWY ON TXWY' AND A BREAK; THEN OUR PARTIAL RESPONSE OF 'CROSS RWY AT TXWY.' THE SUPVR SAID HE WAS NOT GOING TO PURSUE IT SINCE THERE HAD NOT BEEN A CONFLICT; BUT THAT WE SHOULD NOT HAVE CROSSED; AND THAT THE CTLR SHOULD HAVE IMMEDIATELY CORRECTED US BEFORE WE DID. WE WANT TO KEEP OUR OPS SAFE!