B737-300 CREW HAS RWY INCURSION AT SJC AFTER LNDG ON RWY 30L.

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I WAS THE CAPT ON FLT TO SJC. THE FLT WAS A NORMAL FLT UNTIL ON OUR LNDG ROLLOUT AFTER LNDG ON RWY 30L AT SJC. WE TAXIED OFF OF RWY 30L AT TXWY K AND WERE UNDER THE UNDERSTANDING THAT WE WERE CLRED ACROSS RWY 30R WITH AN ACFT THAT HAD BEEN CLRED INTO POS AND HOLD ON RWY 30R. AS WE TAXIED OFF OF RWY 30L ONTO TXWY K WE READ BACK TO THE TWR CTLR INSTRUCTIONS OF CLRED TO CROSS RWY 30R AND TO STAY WITH HIM. BOTH MY FO AND I LOOKED DOWN THE 11000 FT RWY TO KEEP THE TFC IN SIGHT AS WE CROSSED THE RWY. THE NEXT XMISSION THAT WE HEARD WAS OF THE TWR INSTRUCTING THE TFC ON RWY 30R TO CANCEL THEIR TKOF CLRNC. THE SECOND XMISSION FROM THE TWR WAS THEM TELLING US TO HOLD SHORT OF RWY 30R WHEN WE WERE ALREADY HALFWAY ACROSS IT. ONCE ACROSS RWY 30R I STOPPED THE ACFT SO THAT WE COULD EXPRESS TO THE TWR CTLR THAT HE HAD CLRED US TO CROSS RWY 30R AT TXWY K AND THAT OUR READBACK TO HIM WAS IN FACT TO CROSS RWY 30R. HE SAID THAT HE MISSED OUR READBACK AND THEN CLRED US TO TAXI TO THE GATE WITH HIM. ONCE AT THE GATE; I DECIDED TO GIVE THE TWR A PHONE CALL TO FIND OUT WHAT CAUSED OUR COM BREAKDOWN. THE CTLR THAT I TALKED WITH SAID THEY WERE DOWNSTAIRS REVIEWING THE TAPES OF WHAT HAD OCCURRED. I HOPE THAT THE LACK OF COM IN THIS MATTER HAS NOT CAUSED ANY HARDSHIPS.