MD88 FLC CROSSED RWY HOLD LINE AT CLE FOR RWY 5L; THINKING THEY WERE CLRED INTO POS.

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WE PUSHED BACK FROM THE GATE ON A SCHEDULED FLT FROM CLE-CVG. ON CALLING FOR TAXI CLRNC; WE WERE INITIALLY GIVEN; 'CLRED TO RWY 5L VIA VIOLET RTE; HOLD SHORT OF RWY 5R AT TXWY N.' AS WE BEGAN THE TAXI OUT; WE WERE INSTRUCTED TO HOLD SHORT OF TXWY S AND ALLOW THE ACFT EXITING RWY TO PASS IN FRONT OF US; THEN CONTINUE TAXIING DOWN TXWY L; HOLD SHORT OF RWY 5R AT TXWY N. WHILE ON TXWY L; WE STARTED THE SECOND ENG AND COMPLETED THE TAXI AND AFTER START CHKLISTS. WE SWITCHED TO TWR AND COMPLETED BEFORE TKOF CHKLIST; NOTING THERE WERE SEVERAL ACFT ON FINAL FOR RWY 5R. AFTER THE FIRST ACFT LANDED; THE TWR CLRED US TO WHAT WE COULD SWEAR WAS 'ACFT X CROSS RWY 5R AND POS AND HOLD ON RWY 5L; BE READY TO GO.' THE FO READ BACK THE CLRNC AND WE BEGAN TO TAXI OUT; COMPLYING WITH THE CLRNC AS WE UNDERSTOOD IT. TWR THEN CLRED ACFT Y TO CHANGE HIS LNDG CLRNC FROM RWY 5R TO RWY 5L. I COMMENTED TO THE FO AS WE SAW ACFT Y BEGIN TO TURN THAT I HOPED THEY PLANNED ON KEEPING US ROLLING OR THIS WAS GOING TO BE TIGHT. AS WE WERE XING ON TXWY N BTWN RWY 5R AND RWY 5L; I BEGAN SLOWING THE ACFT TAXI AND WAS ASKING THE FO TO 'CHK AND SEE WHAT TWR WANTED US TO DO.' ALL I GOT OUT WAS 'CHK TO SEE' WHEN TWR CALLED AND SAID 'ACFT X YOU WERE SUPPOSED TO BE POS AND HOLD ON RWY 5R.' WE STOPPED THE ACFT COMPLETELY. THE NOSE OF OUR ACFT WAS STILL JUST SHORT OF RWY 5L; BUT WE WERE BEYOND THE HOLD SHORT LINE. ACFT Y WAS GIVEN A GAR AND THEY RESPONDED WITH 'THEY COULD STILL LAND ON RWY 5R' (APPROX 2 1/2 MI OUT). THERE WAS SILENCE FOR ABOUT 5 SECONDS; THEN TWR CLRED THEM TO LAND ON RWY 5R; JUST AS ACFT Y BEGAN EXECUTING A MISSED APCH. TWR THEN CLRED US 'POS AND HOLD ON RWY 5R.' WE TOLD THEM WE WERE UNABLE AND THEY CLRED US FOR 'POS AND HOLD ON RWY 5L;' SHORTLY THEREAFTER CLRING US TO TAKE OFF ON RWY 5L. OUR RETURN TO CVG WAS UNEVENTFUL.