AIR TAXI ACFT DEPARTS WITHOUT IFR RELEASE.

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I WAS FLYING AS CAPT AND AFTER THE TKOF CHK WAS COMPLETED WE HELD AT THE RWY END WAITING FOR OUR IFR CLRNC WHICH THE COPLT WAS OBTAINING ON A MOBILE PHONE. THE CLRNC WAS RECEIVED AND COPIED AS 'CLRED TO THE FORT WAYNE ARPT VIA RADAR VECTORS TO ANNTS; DXO R-217; FWA OH; FWA; CLB TO 3000; EXPECT FL180; DEP 126.85; SQUAWK XXXX.' I WAITED TO HEAR THE COPLT ASK IF WE WERE CLRED AND WHEN HE WAS APPARENTLY SATISFIED WE TOOK OFF. UPON CONTACTING DETROIT WE WERE TOLD TO MAINTAIN VFR AND ISSUED A TFC WARNING. WE MAINTAINED VFR AT 700 AGL AND WERE ISSUED AN IFR CLRNC AFTER 2-3 MINS. IN MY OPINION THE PROBLEM RESULTED FROM LESS THAN CLR INSTRUCTIONS GIVEN AND HAD THERE BEEN APPROPRIATE LANGUAGE USED THERE WOULD HAVE BEEN NO CONFUSION CONCERNING OUR TKOF CLRNC. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO. RPTR STATES PROBLEM WAS THAT CREW BELIEVED THEY HAD A RELEASE. FO ASKED SPECIFICALLY ARE WE RELEASED? CTLR HUNG UP. THEY WERE NOT TOLD NO; SO THEY BELIEVED 'YES.' IT WAS A VERY UNCOMFORTABLE SITUATION BUT HE FELT SAFER TO JUST CIRCLE WHERE IT WAS CLR; EVEN SO LOW; THAN TO LEAVE AREA. THEY OPERATE AT OUTLYING ARPTS FREQUENTLY AND HAVE NO PROBLEMS. HE WILL NOT LET THIS HAPPEN AGAIN.