AN AIRBUS 320 FLC WAS CLRED TO CROSS AN ACTIVE RWY AT SEA. AFTER HEARING AN ACFT CLRED FOR TKOF THE FLC STOPPED IN TIME TO AVOID A POSSIBLE CONFLICT WITH THE DEPARTING ACFT.

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TAXIING ON GND AT SEATAC; WAITING FOR DEP; GND CTL TOLD US TO TAXI TO RWY 34R; HOLD SHORT OF RWY 34R AT TXWY Q. WE GOT IN LINE (IT WAS AFTERNOON) BECAUSE IT WAS BUSY; AND WAITED OUR TURN. FOR RWY 34R; ATC WAS USING FULL LENGTH AND INTXN Q TKOFS. ATC HAD GIVEN AN ACFT INSTRUCTIONS TO TAXI INTO POS AND HOLD FULL LENGTH RWY 34R; AND HE DID SO; HOLDING IN POS. TWR THEN TOLD US TO CROSS RWY 34R AT TXWY Q AND HOLD SHORT OF RWY 34L. AS SOON AS HE CLRED US TO CROSS RWY 34R AT TXWY Q; HE CLRED THE ACFT HOLDING FULL LENGTH TO TAKE OFF! I IMMEDIATELY STOPPED AND QUERIED THE TWR CTLR. I WAS ABLE TO STOP IN TIME TO AVOID XING THE HOLD SHORT LINE; AND WATCHED AS THE LARGE TURBOPROP 'WHIZZED BY!' ATC OBVIOUSLY FORGOT HE HAD CLRED ME TO CROSS. ATC TOLD ME 'SORRY' AND 'THANKS;' AND THEN CLRED ME TO CROSS RWY 34R. THE REST WAS UNEVENTFUL. HAD I NOT BEEN ALERT; I'M SURE THIS WOULD HAVE BEEN A SIT. AN ABORT AT BEST BY THE ACFT TAKING OFF AND/OR RWY INCURSION BY ME. VERY DANGEROUS RWY CONFIGN THEY WERE OPERATING -- PRONE TO ERROR -- ESPECIALLY DURING REDUCED VISIBILITY.