A PERCEIVED RWY INCURSION AT SWF; NY.

Narrative

OUR B727 WAS READY FOR TAXI AFTER PUSHBACK AND ENG START ON TXWY L; HOLDING JUST SHORT OF RWY 9/27. COMPANY SUPPLIED INFO INCLUDED A CAUTION FOR THIS ARPT 'ASSURE POSITIVE ATC CLRNC TO CROSS RWY 27 AT TXWY L PRIOR TO TAXIING FROM THE RAMP AREA.' AFTER MY STANDARD CALL FOR TAXI; GND CTL RESPONDED; 'ACR X CLRED TO TAXI RWY 9 VIA TXWYS L; A2; A TO RWY 9.' TO WHICH I RESPONDED; 'ACR X IS CLRED TO RWY 9 VIA TXWYS L; A2; A...UNDERSTAND CLRED TO CROSS RWY 9/27.' THERE WAS NO OTHER MOVEMENT ON THE ARPT. NO OTHER ACFT WAS TALKING TO GND. WE TAXIED ACROSS RWY 9/27 AFTER CLRING BOTH DIRECTIONS AND BEGAN OUR PRE-TKOF CHKS. THE GND CTLR THEN ASKED US TO CALL HIM ON LAND LINE AND HE GAVE US A NUMBER TO CALL. THE CAPT CALLED THE TWR WHICH ACCUSED US OF A RWY INCURSION. WE REITERATED OUR RESPONSE TO HIS INSTRUCTIONS THAT WE WERE CLRED TO CROSS; AT THAT HE MADE WHAT WE THOUGHT WAS GARBLED RESPONSE OF 'ROGER.' HE ADMITTED THAT HE HAD NOT LISTENED CLOSELY TO OUR READBACK. THE CREW FELT AS IF WE WERE BAITED INTO THIS INCURSION. WE READ BACK WHAT WE BELIEVED WE WERE CLRED TO CROSS BECAUSE THERE CAN BE CONFUSION SINCE WE PUSHED BACK SO CLOSE TO THE HOLD SHORT. WHY GIVE US THE TAXI INSTRUCTIONS IF HE WANTED US TO HOLD SHORT. WHY NOT SAY 'HOLD SHORT.' THE SCARY ASPECT OF THIS INCIDENT WAS THAT WE HAD READ BACK THE CAUTION AND STILL GOT MISLEAD BY THE TWR. I FLEW ON THIS SAME PAIRING THE NEXT 2 DAYS AND BOTH MYSELF AND A DIFFERENT GND CTLR WERE MUCH MORE DEFINITIVE.