AN ALLEGED RWY INCURSION AFTER 3 CREW MEMBERS ALL HEAR A 'CLR TO CROSS RWY 35L; LNDG TFC ON FINAL' FROM TWR CTLR AT LIMC; FO.

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AFTER PUSHBACK AND ENG START AT MILAN'S MALPENSA (LIMC); WAS GIVEN INSTRUCTIONS TO TAXI S ON TXWY Y TO RWY 35R AND TO HOLD SHORT OF RWY 35L IN TXWY F. PRIOR TO REACHING TXWY U (L5) FLT WAS INSTRUCTED TO GIVE WAY TO LNDG TFC EXITING RWY 35L AT TXWY F. AFTER GIVING WAY; APRON CTL SAID 'CONTINUE AND HOLD SHORT OF RWY 35L ON TXWY F AND CONTACT TWR 128.35.' AFTER HOLDING FOR APPROX 2 MINS ON TXWY F WITH THE PARKING BRAKES SET; WE RECEIVED A CLRNC TO CROSS RWY 35L AT TXWY F; 'CLRED TO CROSS RWY 35L; LNDG TFC ON FINAL.' THE FO #2 (PF) RESPONDED 'ROGER; CLRED TO CROSS RWY 35L; TFC IN SIGHT;' AT WHICH TIME I REPLIED; 'I HEARD CLRED TO CROSS RWY 35L; FOLLOWED BY FO #1 (RELIEF PLT) 'THAT'S WHAT I HEARD ALSO; CLRED TO CROSS.' AFTER XING 1/2 WAY ACROSS THE RWY; THE TWR CAME BACK; 'YOU WERE NOT GIVEN CLRNC TO CROSS RWY 35L.' THE FO SAID WHAT WAS READ BACK PRIOR TO STARTING ACROSS AND THE CTLR SAID 'NEGATIVE; TFC 4 MI ON FINAL. A RPT WILL BE FILED.' THE TWR ASKED THE LNDG TFC IF A GAR WAS NEEDED; WHICH THEY ANSWERED 'NEGATIVE.' AFTER TURNING R ONTO TXWY C; I NOTICED THE LNDG TFC TOUCHING DOWN ONTO RWY 35L. WE DEPARTED TO IAD WITHOUT FURTHER INCIDENT. SUPPLEMENTAL INFO FROM ACN 554415: 1/2 WAY ACROSS; TWR MADE AN UNINTELLIGIBLE CALL. TWR THEN TOLD ACFT ON FINAL TO GO AROUND BECAUSE OF US. HOWEVER; THE TFC CONTINUED. TWR THEN SAID 'YOU WERE NOT CLRED TO CROSS; I TOLD YOU NOT TO CROSS; TWICE.' ALL 3 PLTS WERE ON THIRD TRIP TO LIMC THIS MONTH. CTLR CLRLY SAID TO CROSS THE RWY; THERE WAS NO DOUBT AMONGST ANY OF US. THE CTLR MAY HAVE MEANT TO SAY DON'T CROSS; BUT HE SAID SOMETHING ELSE IN ENGLISH.