COMMUTER FLT DEPARTS WITH WX INFO WRONGLY INTERPRETED AND BELIEVE THEY ARE LEGAL. THEY ARE NOT.

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THE SCHEDULED DEP TO ITHICA; NY; WAS DELAYED DUE TO OUR INBOUND FLT'S LATE ARR AT PHILLY. OUR WX WE HAD IN THE ACFT INCLUDED THE WX RPTS AND FORECASTS FOR ITHICA; OUR NEXT DEST. THE WX WAS FORECAST TO BE; AT OUR ARR TIME; 1 1/2 MI VISIBILITY IN RAIN AND FOG: NO WORSE. WE REVIEWED THIS INFO ENRTE TO PHILLY BEFORE OUR NEXT DEP TO ITH WHICH WOULD LEAVE AS SOON AS WE LANDED (LATE) IN PHILLY AND BOARDED FUEL AND PAX. AS WE ARRIVED IN PHL; I TOOK CARE OF THE BUSY WORK (CHKLISTS; CLRNCS; ATIS; WT AND BAL PRELIMINARY PAPERWORK). AS THE CAPT WENT INSIDE TO GET UPDATED WX. HE ARRIVED BACK AND SAID 'WE'RE GOOD TO GO; WX IS FORECAST TO BE 1 1/2 MI ON THE TERMINAL FORECAST (WELL ABOVE THE ILS REQUIREMENT OF 3/4 MI VISIBILITY). BUT; WE SAW A 'CHANCE OCCASIONAL VISIBILITY 1/2 RAIN AND FOG.' I ASKED; 'CAN WE GO WITH THIS?' HE SAID YES; THE CTLING WX IS THE BODY OF THE TERMINAL FORECAST; FORECASTING THE MOSTLY CONTINUOUS 1 1/2 MI VISIBILITY. WE DISCUSSED IT; LOOKED AT ALTERNATE ARPTS NEARBY WITH VISIBILITY FORECASTS OF 2 MI; ETC; AND AGREED TO GO. REST OF FLT WITHOUT INCIDENT; ARRIVED AT ITH WITH WX OF 2 1/2 MI; RAIN AND FOG. IT CONCERNED ME; THOUGH; AS WELL AS THE CAPT; IF THE 'OCNL' AND 'CNNC' WEREN'T CTLING ALSO. WE RESEARCHED IT; AND THIS GREY AREA WAS FINALLY DECIDED AS CTLING BY THE COMPANY; AND I AGREED. WHY DID WE MAKE THIS MISTAKE? RUSH; BEHIND SCHEDULE. OUR MINDSET WAS THAT THE TERMINAL FORECAST BODY WAS CTLING; WRONG. WE ALL NEED TO KEEP AT THE COMPANY FLT MANUALS; FARS; ETC; AND BE ASSERTIVE IN TURNING GREY AREAS INTO BLACK AND WHITE FOR OURSELVES AND FELLOW PLTS.