ACR QUESTIONS WHETHER THEY CROSSED RWY WITHOUT CLRNC AT LAX.

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ON GND AT LAX; HOLDING ON TXWY B SHORT OF TXWY P. A DC8 FOREIGN CARGO CARRIER WAS HOLDING ON TXWY P IMMEDIATELY AHEAD OF US. GND CLRED THE DC8 TO CROSS RWY 25R HOLD SHORT OF RWY 25L. WE WERE THEN CLRED TO CROSS RWY 25R ON TXWY P HOLD SHORT OF RWY 25L. WE FOLLOWED THESE INSTRUCTIONS. THE TWR LATER (AFTER WE HAD PARKED) INFORMED US; HOWEVER; THAT OUR INSTRUCTIONS WERE TO TURN ON TXWY P HOLD SHORT OF RWY 25R AND THAT THE FO HAD ACKNOWLEDGED THIS. THE FO AND I FIRMLY BELIEVE THAT OUR CLRNC WAS 'CLRED TO CROSS RWY 25R.' BEFORE XING RWY 25R; I CHKED TO SEE IF THE RWY AND APCH PATH TO RWY 25R WAS CLR. THEY WERE AND NO CONFLICT WAS INVOLVED. THE TWR NEVER INSTRUCTED US TO STOP. WE CROSSED RWY 25R CLOSE BEHIND THE DC8 AND HOLD SHORT OF RWY 25L BEHIND THE DC8. DURING THE ENTIRE TAXI EVOLUTION THERE WAS A GREAT DEAL OF RADIO TFC WITH ACFT HAVING DIFFICULTY XMITTING TO GND CTL. SEVERAL FOREIGN CARRIERS WERE ON GND FREQ HAVING DIFFICULTY UNDERSTANDING INSTRUCTIONS; CLUTTERING GND FREQ; AND ADDING TO THE CONFUSION ON GND CTL FREQ. THE GND CTLR FINALLY TOLD EVERYONE TO KEEP QUIET UNTIL HE CALLED THEM.