A DC8 CREW; TAXIING TO RAMP AFTER LNDG AT TYS; TAXIED ACROSS AN ACTIVE RWY WITHOUT CLRNC.

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KNOXVILLE APCH; TWR; GND CLRED US FOR A VISUAL APCH TO KNOXVILLE (TYS) RWY 23R. THE FO FLEW THE APCH AND LNDG AND I TOOK THE ACFT BACK AT THE END OF THE ROLLOUT. I TURNED L AT THE END; THEN L AGAIN ONTO PARALLEL TXWY B. I ADDED PWR AS THERE IS AN UPHILL GRADE IN THAT DIRECTION. THE CTLR HAD CLRED US TO TAXI TO AND HOLD SHORT OF THE APCH END OF RWY 23R. WE PROCEEDED ALONG; NOTING A DC9 LNDG ON RWY 23R. AS WE TAXIED; WE DID OUR AFTER LNDG CHKLIST. THE CTLR MADE A RADIO CALL TO THE OTHER PLANE TO MAKE A 180 DEG TURN ON THE RWY AND TAXI TO THE RAMP (UNSPOKEN BUT UNDERSTOOD TO BE VIA TXWY G7); AND I THOUGHT HE CLRED US IN THE SAME CALL; TO CROSS RWY 23R AT THE END AND TAXI IN (SAME RAMP). THE ADDED PWR HAD GIVEN US A GOOD SPD ON TXWY B AND SO WE REACHED THE END FAIRLY QUICKLY. UPON ROUNDING THE CORNER AT TXWY B AND B8; I NOTICED THE DC9 TURNING OFF ON G7; WHICH FIT WITH MY UNDERSTANDING OF WHO WAS TO GO WHERE. I CROSSED THE END OF RWY 23R AND ONTO TXWY G8. THEN THE CTLR SAID ON THE RADIO THAT WE WEREN'T SUPPOSED TO HAVE DONE THAT. I SPOKE ON A PHONE WITH THE CTLR AFTER WE WENT IN; AND EXPLAINED WHAT I THOUGHT WE WERE CLRED AND APOLOGIZED FOR ANY MISUNDERSTANDING. THE CTLR SOUNDED PEEVED BUT ACCEPTED MY APOLOGY AND SAID HE WOULDN'T DO ANYTHING ABOUT IT THIS TIME; BUT WILL NEXT TIME. HE MAINTAINS HE HAD NOT CLRED US ACROSS; AND HE MAY BE RIGHT; WE WERE TIRED. MAJOR CONTRIBUTING FACTORS TO THIS INCIDENT: THIS IS AN OVERNIGHT OP WITH AN XA30 PM HOTEL PICKUP TIME; A FLT INTO A SORT WITH A WAIT OF 4+ HRS; FOLLOWED BY A FLT OUT. THIS IS FATIGUING EVEN FOR THOSE WHO THINK THEY ARE USED TO IT. THERE IS NO FACILITY AT ANY OF OUR SORTS TO GET ANY REAL REST (RECLINERS ONLY); SO THE FATIGUE REALLY IS THERE. THERE IS A PSYCHOLOGICAL TERM; WHICH ESCAPES ME RIGHT NOW; FOR THE MIND TAKING WHAT WAS HEARD AND TURNING INTO WHAT ONE EXPECTS OR WANTS TO HEAR. THAT MAY WELL HAVE HAPPENED TO ALL 3 OF US THIS MORNING. MIX WITH FATIGUE; AND THE COMBINATION CAN BE SCARY.