POSSIBLE UNAUTHORIZED RWY XING BY ACR.

Narrative

HOLDING SHORT OF RWY 36R WITH SEVERAL OTHER ACFT OF SAME COMPANY HOLDING SHORT OF 36R AT OTHER INTXNS UP AND DOWN RWY. HAD BEEN WAITING SEVERAL MINS FOR A BREAK IN THE TKOF ACFT ON 36R. HEARD TWR CLR ACFT INTO POS ON 36R TO HOLD WHILE XING ACFT DOWN FIELD. HEARD TWR CLR A WDB ON MY R TO CROSS. WE STARTED TO COME UP ON THE PWR IN PREPARATION FOR XING; HEARD A CLRNC TO CROSS BUT WASN'T SURE IT WAS FOR US. COPLT IMMEDIATELY READ BACK THE CLRNC TO CROSS. THE WDB WAS XING THE RWY AND THE TWR ISSUED A CLRNC FOR ANOTHER ACFT TO CROSS SO I CROSSED THE RWY. ABOUT HALF WAY ACROSS; THE COPLT SAID THAT THE TWR HAD CALLED US BY THE WRONG CALL SIGN. I WAS NOT HAPPY TO HEAR THAT STATEMENT. WE CROSSED THE RWY WITHOUT INCIDENT AND I BELIEVE WE PROBABLY WERE THE ACFT HE INTENDED TO CLR ACROSS; BUT WHY DO PEOPLE MAKE SUCH ASSUMPTIONS? THIS IS A VERY WELL QUALIFIED PLT WITH YRS OF EXPERIENCE; AND YET HE DID NOT RESPOND PROPERLY; AND QUESTION THE TWR CTLR ON THAT CALL SIGN. I'VE ALWAYS TRIED TO MAKE SURE THAT I HAVE THE PROPER INFO AND HAVE NO HESITANCY TO QUESTION THE CTLR. I'VE TRIED TO ENCOURAGE MY COPLTS TO DO LIKEWISE AND WILL CONTINUE TO DO SO. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THERE WAS NO CONFLICT BTWN ACFT OR WITH VEHICLE. NORMAL FOR DFW TWR TO LAND SEVERAL ACFT ON THE OUTER RWY AND HOLD THEM SHORT OF THE INNER UNTIL THEY GET A BUNCH TO CROSS. THEN THEY STOP DEPS ON INNER PARALLEL RWY WHILE THEY CROSS ALL THOSE WAITING TO GET TO THE RAMP. DID NOT REVIEW INCIDENT WITH ATC AND THINKS CTLR MEANT FOR THEM TO CROSS; BUT USED DIFFERENT TRIP NUMBER. FO TOLD PIC THAT THEY WERE CLRED TO CROSS AND DID NOT MENTION WRONG CALL SIGN PROBLEM UNTIL HALF WAY ACROSS. SHOULD HAVE ASKED TWR CTLR TO CLARIFY IF CLRNC WAS FOR THEM.