UNAUTH RWY ENTRY.

Narrative

'CLRED TO CROSS RWY 6L CONTACT GND ON THE OTHER SIDE;' OR 'HOLD SHORT OF RWY 6L FOR LNDG TFC.' SEEMS PRETTY STRAIGHT FORWARD; BUT I CAN'T TELL YOU FOR SURE WHAT THE CLRNC WAS. WE WERE UP ALL NIGHT ON A FREIGHTER FLT LAX- ANC; AND I WAS VERY TIRED. WE WERE ON LNDG ROLLOUT IN FULL REVERSE TRYING TO STOP A HVY FREIGHTER ON RWY 6R. THE CAPT WAS TALKING TO ATC ON WHETHER ANOTHER 747 WAS BLOCKING THE INTXN WE WERE PLANNING TO TURN OFF AFTER WE CROSSED RWY 6L. AFTER COMPLETING THE LNDG ROLL; THE CAPT TOOK CTL OF THE ACFT; MADE THE HIGH SPD TURNOFF; AND CROSSED RWY 6L. AS WE CROSSED; WE SAW A CONVAIR ON SHORT FINAL WHO WAS TOLD TO GAR. A SUBSEQUENT PHONE CALL TO THE TWR HAD THE CTLR CLAIMING HE NEVER CROSSED US; AND THE CAPT CLAIMING HE READ BACK; 'CROSS THE L AND CONTACT GND.' ATC SAID THEY WERE NOT GOING TO 'MAKE AN ISSUE OUT OF IT;' SO I GUESS THE TAPES ONLY KNOW FOR SURE. THIS POTENTIAL CONFLICT WAS COMPLICATED BY A LOT OF VERBIAGE DURING A CRITICAL PHASE OF FLT. FULL REVERSE WAS BLARING; THE PF WAS BRAKING AT MAX LNDG WT; THE SO IS MONITORING ENG INSTS AND MAKING CALLOUTS; AND THE CAPT IS BEING ASKED SEVERAL QUESTIONS ABOUT OUR TURNOFF; ETC. THE CAPT BET HIS LIFE WE WERE CLRED TO CROSS. I JUST WISH CTLRS WOULD UNDERSTAND THAT THE LAST 3000 FT OF A LNDG ROLL ARE ONE OF THE BUSIEST TIMES OF A FLT. ONLY VERT CRITICAL XMISSIONS SHOULD BE MADE TO A CREW DURING THIS TIME. SUPPLEMENTAL INFO FROM ACN 273721: AS WE WERE ROLLING OUT I HEARD THE TWR SAY 'CLRED TO CROSS RWY 6L CONTACT GND CTL ON 121.9 ON THE OTHER SIDE.' I RESPONDED AND PROCEEDED TO CROSS RWY 6L AT THE END OF RWY 6R. AS THE TXWY OFF RWY 6R (TXWY C) IS AN ANGLING HIGH SPD TXWY; I WAS UNABLE TO LOOK DOWN RWY 6L TO THE L UNTIL I WAS ON RWY 6L. AT THAT TIME I SAW A CONVAIR ABOUT TO LAND. VERY STRONGLY THAT THE TWR CLRED US TO CROSS RWY 6L. THE TWR CHIEF THINKS THAT WE WERE TOLD TO HOLD SHORT. HUMAN FACTORS: IF I HEARD THE INSTRUCTIONS WRONG; IT COULD BE BECAUSE I WAS TIRED. WE HAD DEPARTED LAX AT XA34 AM AND HAD FLOWN NONSTOP TO ANC.