POTENTIAL GND CONFLICT AS ACR MLG CROSSES RWY. MULTIPLE RWY OP PARALLEL RWYS.

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WHILE TAXIING TO RWY 4R AT LOGAN INTL; WE WERE TOLD TO HOLD SHORT OF RWY 4L AND CONTACT TWR. WE DID SO AND WERE INFORMED OF TFC ON A 1 1/2 MI L BASE TO RWY 4L AND WERE CLRED TO CROSS RWY 4L AND TAXI TO RWY 4R. BEFORE XING RWY 4L; WE SAW AN ACFT ON FINAL THAT COULD NOT HAVE BEEN THE PREVIOUSLY RPTED TFC. BECAUSE OF THE WX AND VISIBILITY; THIS ACFT LOOKED AS IF IT WERE ON FINAL TO THE RWY WE WERE CLRED TO CROSS. WE HELD OUR POS AND QUESTIONED TWR ABOUT THE TFC. HE INFORMED US THE TFC WAS ON FINAL TO RWY 4R; NOT RWY 4L. BECAUSE OF THE DISTR OF THE PERCEIVED TFC CONFLICT; I FORGOT THE ORIGINALLY CALLED OUT TFC AS I STARTED TO CROSS RWY 4L. AS WE STARTED TO CROSS; WE WERE TOLD TO SWITCH TO THE OTHER TWR FREQ. WE WERE ALMOST CLR OF RWY 4L WHEN I LOOKED R TO CHANGE FREQS; LOOKED UP AND SAW THE ORIGINAL TFC; A COMMUTER BEECH 1900 PASSING VERY CLOSELY BEHIND US. THERE WAS NO CALL FROM TWR; OR FROM THE OTHER ACFT; BUT I'M SURE THE PAX ON THE R SIDE OF THE COMMUTER GOT A MUCH CLOSER LOOK AT OUR ACFT'S TAIL THAN I WANTED THEM TO HAVE.