ACR CROSSED ACTIVE RWY WHILE OTHER ACR WAS STARTING TKOF ROLL. OPERATIONAL ERROR.

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UNDER CLEAR WEATHER CONDITIONS; LANDED RWY 9R AT ATL. WHILE EXITING THE RWY TWR WAS ENGAGED IN A HIGH LEVEL OF DISCUSSIONS WITH SEVERAL OTHER AIR CARRIER ACFT RELAVENT TO A PROBLEM WITH JAX CENTER HAVING TO DO WITH TFC SATURATION AND THE NEED TO CLEAR THESE ACFT FOR TKOF AS SOON AS POSSIBLE. WHEN WE CLRED THE RUNWAY; THE COPLT UNDERSTOOD THE TWR TO SAY 'CLRED TO CROSS RUNWAY 9L' AND HE READ BACK 'ROGER; CLRED TO CROSS 9L' HEARING NO FURTHER COMMENTS; WE PROCEEDED ACROSS THE RWY. I NOTICED AT THE TIME OF XING AN AIR CARRIER JUST BEGINNING ITS TAKEOFF ROLL. NO EVASIVE ACTION WAS NECESSARY; AS WE WERE APPROX. 7000'-8000' DOWN A 10000' RWY WITH MORE THAN ADEQUATE SEPARATION. SUBSEQUENT DISCUSSIONS WITH THE TWR SUPERVISOR ON THE PHONE INDICATED THEY HAD LISTENED TO THE TAPES; AND THE CTLR HAD SAID 'HOLD SHORT OF 9L' AND WE IN FACT HAD READBACK 'CLRED TO CROSS 9L' AND THE CTLR HAD MISSED THE INCORRECT READ BACK. HIS INDICATION TO ME WAS IT WAS AN OPERATIONAL ERROR ON THEIR PART. I SUSPECT THE COPLT MIGHT HAVE HEARD THE CLRNC FOR THE ACFT ON THE TAKEOFF ROLL AND THOUGHT IT WAS FOR US. - UNABLE TO GET THE ACFT VOICE RECORDER AS THE ACFT DEPARTED IMMEDIATELY. SUPPLEMENTAL INFORMATION IN ACN 83730: AS WE EXITED 9R ON A HIGHSPEED TAXIWAY TWR MADE A XMISSION TO US AND THE F/O READ BACK 'OUR IDENT CLRED TO CROSS 9L' AS WE HAD STATIC ON ONE OF THE RADIOS THAT TWR FREQ 119.1 WAS ON; I HAD BOTH RADIOS ON 119.1 WITH VOLUME UP AT NO TIME AFTER I READ BACK THE XING CLRNC DID THEY SAY ANYTHING ELSE.