A TAXIING F28 FLC CROSSES ACTIVE RWY 34R AFTER LNDG WHICH CREW ALLEGED WAS THE CLRNC GIVEN. TWR DISPUTED CLAIM AS TFC HAD JUST DEPARTED IN FRONT OF THE F28 AND ONE PULLING INTO POS AT SEA.

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ON LNDG ROLLOUT; SEATAC RWY 34L; MYSELF AND THE CAPT BOTH HEARD THE FOLLOWING CLRNC; 'ACR X; MAKE THE R TURN;' FOLLOWED BY; 'THE SECOND R; CROSS RWY 34R; CONTACT GND .7;' FOLLOWED BY 'WHEN CLR' OR 'UPON ENTERING TXWY B.' AS INSTRUCTED; WE TURNED ONTO THE REVERSE HIGHSPD WHEN WE SAW A B737 LIFTING OFF IN FRONT OF US. WE WERE NOT OVER THE HOLD LINE WHEN HE PASSED; BUT WE THOUGHT IT WAS STRANGE THAT THE CLRNC WAS SO CLOSE TO THE DEPARTING ACFT. AFTER THAT ACFT PASSED; WE VISUALLY CLRED L AND R AND CROSSED RWY 34R. WE SAW AN MD80 ON THE DEP AND PULLING INTO POS. JUST AFTER WE CROSSED THE CTRLINE WE HEARD THE LCL CTLR SAY 'ACR X; CONTINUE HOLDING SHORT!' I REPLIED THAT IF THERE HAD BEEN A HOLD SHORT CLRNC AFTER OUR XING CLRNC IT HAD BEEN BLOCKED. WE CLRED RWY 34R; WERE SENT TO GND FREQ; WHO TOLD US TO CALL THE TWR AND WE BLOCKED IN. ON THE PHONE; THE TWR SAID THAT THE LCL CTLR AND SUPVR BOTH CLAIMED WE HAD NOT BEEN CLRED TO CROSS. THEY ADVISED US THAT THEY WOULD PULL THE TAPE; AND THAT WE COULD CALL THEM ON THE RETURN FROM OUR NEXT ROUND-TRIP. WHEN WE CALLED THEN BACK; THEY SAID; 'OH; FORGET IT; WE COULDN'T UNDERSTAND ANYTHING ON THE TAPE.' THERE WAS NO IMMINENT DANGER DURING THE INCIDENT AS WE WERE NOT IN THE RWY WHEN THE B737 PASSED; BUT ALL INVOLVED WERE VERY AGITATED. I BELIEVE THAT THE RWY LAYOUT AT SEA FORCES CTLRS TO CUT THINGS TOO CLOSE; INCLUDING A FREQUENT LACK OF STANDARD PHRASEOLOGY (IN THIS INSTANCE; NO TXWY NAMES WERE USED IN THE INITIAL CLRNC).