B727-200 CREW IS ACCUSED OF A RWY INCURSION AFTER LNDG AT MIA.

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AFTER LNDG IN MIAMI ON RWY 9R WE WERE ASKED BY THE TWR CTLR WHAT WAS OUR GATE. AFTER LEAVING THE RWY THE CTLR CALLED US BACK AND WE ALL UNDERSTOOD THAT HE SAID 'CROSS RWY 12 AND STAY WITH ME.' I DID NOT STOP THE AIRPLANE BECAUSE TO US; WE WERE CLR TO CROSS RWY 12. WHILE CROSSING RWY 12 WE NOTICED THE LNDG LIGHTS (ALL ON) OF AN AIRPLANE THAT WAS AT THE END OF RWY 12. THERE WE HAD A FEW SECONDS OF CONFUSION. AN ACR Y AIRPLANE WAS TOLD TO ABORT; BUT WE WERE ALREADY ON THE N SIDE OF RWY 12. HOLDING IN POSITION WAITING FOR AN AIRPLANE THAT WAS TAXING WBOUND TO PASS BY AND FOR A FREQ CHANGE. AT THAT TIME THE CTLR SAID THAT HE HAD NOT CLRED US TO CROSS THE RWY 12 AND HE SWITCHED US TO GND CTL FREQ. GND CTL CLRED US TO GATE VIA P-W-Y-N. MOMENTS LATER THE GND CTLR CALLED US BACK AND TOLD US TO COPY A PHONE NUMBER AND TO CALL THAT NUMBER FROM THE GATE. I CALLED THE NUMBER; I SPOKE TO TWR SUPVR. WE TALKED ABOUT WHAT HAD HAPPENED. HE TOLD ME THAT TO HIS UNDERSTANDING WE HAD A RWY INCURSION; THAT AN INVESTIGATION WAS PROBABLY ON THE WAY. HE ASKED MY LICENSE NUMBER AND MY PHONE NUMBERS. HE SAID HE WAS GOING TO CALL ME LATER. ABOUT 45 MINS LATER HE CALLED AT MY COMPANY'S HEADQUARTERS; HE SPOKE TO ME AND MY CHIEF PLT. HE INFORMED ME AND THE CHIEF PLT THAT AN INVESTIGATION WAS INITIATED. I'VE BEEN OPERATING IN AND OUT OF MIAMI ARPT FOR MORE THAN 20 YRS WITHOUT ANY PREVIOUS INCIDENTS. IN MY 20 PLUS YRS OF AIRLINE OP IN ALL SEATS (FLT ENGINEER; CO-PLT; CAPT) AND ALMOST AROUND THE WORLD; THIS IS THE FIRST TIME THAT I HAVE HAD THIS TYPE OF INCIDENT; BECAUSE I UNDERSTAND HOW CRITICAL IT COULD BE TO CROSS AN ACTIVE RWY. THE BEST OF MY KNOWLEDGE WE WERE CLR TO CROSS RWY 12. SUPPLEMENTAL INFO FROM ACN 520885: WE WERE CLRED FOR AN ILS APCH AT RWY 9R. A CONTRIBUTING FACTOR MAY HAVE BEEN FATIGUE. WE HAD BEEN FLYING SINCE XA00 THE NIGHT BEFORE. DESPITE THE FACT THAT OUR DUTY TIME WAS ONLY ABOVE 10 HRS; THAT WE WERE OPERATING AT ABNORMAL HRS DIMINISHED ATTENTION SPAN. TWR NEVER ACKNOWLEDGED A READBACK FROM US ALSO CREATED A CONFUSION. SINCE WE ASSUMED THE INSTRUCTIONS TO BE TO CROSS 12 AND REMAIN WITH THE TWR; I BELIEVE THAT THE CONCENTRATION IN OUR BEHALF AT THE MOMENT SHOULD HAVE BEEN A LITTLE BETTER. AND THE CTLR'S ACKNOWLEDGEMENT OF A CORRECT READBACK WOULD HAVE ALSO HELPED IN CORRECTING OUR WRONGDOING.