FLC OF A DC3 MADE UNAUTH XING OF AN ACTIVE RWY DURING TAXI IN AFTER LNDG AND SUBSEQUENTLY STOPPED BEFORE XING ANOTHER ACTIVE RWY DUE TO A LNDG FALCON 900. THE TWR SENT AROUND A PIPER CHEROKEE DUE TO THE UNAUTH XING OF THE FIRST RWY. RPTING CAPT SAYS THAT HE WAS FOLLOWING TWR INSTRUCTIONS; BUT TWR SAYS NO.

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WHILE TAXIING IN AFTER LNDG ON RWY 35 AT SLC; I WAS INSTRUCTED BY SLC TWR ON 118.3 MHZ TO 'CROSS RWY 32 AND HOLD SHORT OF RWY 34R.' AS I CROSSED RWY 32; SLC TWR FRANTICALLY TOLD A PIPER CHEYENNE TO 'GO AROUND' AND ASKED MY ACFT WHY WE CROSSED RWY 32. WHEN MY COPLT TOLD THE CTLR WE WERE INSTRUCTED TO CROSS; THE CTLR BECAME VERY IRATE AND TOLD MY ACFT TO 'CROSS RWY 34R; CONTACT GND ON THE W SIDE.' BEFORE I ENTERED RWY 34R; I LOOKED L AND SAW A FALCON 900 ABOUT TO TOUCH DOWN ON THE NUMBERS; SO I LOCKED THE BRAKES TO AVOID BEING HIT BY THE FALCON. SLC TWR THEN CALLED MY ACFT AND WE WERE INSTRUCTED TO CALL THEM ON 119.05 MHZ FOR CLRNC TO CROSS RWY 34R. AFTER WE CROSSED RWY 34R; SLC GND INSTRUCTED US TO CALL THEM ON THE PHONE AFTER SHUTDOWN. I CALLED THE SLC TWR CHIEF AND ASKED HIM TO PLEASE REVIEW THE TAPES AND I WOULD CALL BACK LATER. I ASKED MY COPLT AND A CARGO LOADER; WHO WAS WITH US; WHAT THEY HEARD. THEY SAID THEY AGREED WITH MY RECOLLECTIONS. WHEN I CALLED THE SLC TWR CHIEF AGAIN; HE SAID HE HAD REVIEWED THE TAPES AND WAS CONVINCED WE DISREGARDED INSTRUCTIONS AND CROSSED ACTIVE RWYS WITHOUT A CLRNC.