C525 FLT CREW DEPARTING NON TWR ARPT REQUESTS A POPUP IFR CLRNC. CTLR ISSUED A CLB TO 3000 FT; BUT IS REFUSED BY PLT DUE TO TERMINOLOGY.

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I WAS FLYING CAPT IN OUR COMPANY'S CITATION 525; ALONG WITH A COMPANY EMPLOYED SIC. I HAD DEPARTED EOK ENRTE TO PWK. I FILED AN IFR FLT PLAN FROM EOK TO PLANO INTXN; OBK VOR; DIRECT TO PWK ARPT; FL210. THE WX AT EOK WAS RPTING AN OVCST CEILING OF 2400 FT AGL AND VISIBILITY OF 8 MI. I ELECTED TO DEPART EOK VFR AND PICK UP MY IFR CLRNC WITH ZKC ON FREQ. AFTER DEP; I CLBED TO 2500 FT MSL IN ORDER TO STAY UNDER THE OVCST LAYER AT 3100 FT MSL. AT 2500 FT; THE SIC CALLED FOR OUR CLRNC TO PWK; INFORMING CTR THAT WE HAD JUST DEPARTED EOK AND WE WERE AT 2500 FT. CTR TOLD US TO STAND BY WHILE SHE WORKED WITH ZAU TO COORDINATE OUR FLT WITH AN ACFT ARRIVING AT BRL ARPT. A COUPLE OF MINS PASSED AND CTR TOLD US TO TAKE A HDG OF 090 DEGS AND CLB TO AN ALT OF 3000 FT MSL. MY SIC REPLIED THAT WE WERE ON THE HDG 090 DEGS; BUT WE WERE UNABLE TO CLB TO 3000 FT MSL BECAUSE WE WOULD NOT BE ABLE TO STAY VFR. CTR STATED; 'I HAVE RADAR CONTACT WITH YOU; TAKE 090 DEG HDG AND CLB TO 3000 FT.' I TOLD THE SIC NOT TO ACCEPT HER INSTRUCTION UNTIL SHE GAVE US AN IFR CLRNC. THE SIC CALLED CTR BACK AND ASKED IF SHE WAS GIVING US AN IFR CLRNC. CTR SAID 'NXXXX; CLB TO 3000 FT; YOU ARE WITH ME.' THE SIC SAID; 'WE ARE ON THE HDG OF 090 DEGS AND WE WILL STAY AT 2500 FT AND WAIT FOR OUR IFR CLRNC.' THEN CTR CALLED BACK; 'OK NXXXX; YOU ARE CLRED TO PWK VIA AS FILED; FOR NOW FLY HDG 90 DEGS AND CLB TO 3000 FT.' UPON HEARING THE IFR CLRNC; I PROMPTLY CLBED TO 3000 FT. DURING THIS BRIEF TRANSACTION OVER THE RADIO; THE CTLR BECAME VERY AGITATED WITH OUR INSISTING ON HAVING AN IFR CLRNC BEFORE ENTERING IFR CONDITIONS. AT FIRST; I THOUGHT MAYBE THE CTLR HAD JUST FORGOTTEN TO GIVE US A CLRNC. HOWEVER; AFTER STATING OUR CONCERNS; SHE CAME BACK TO US WITH THE COMMENT OF; 'CLB TO 3000 FT; YOU'RE WITH ME;' INDICATING TO ME THAT MAYBE SHE WASN'T UNDERSTANDING REQUIREMENT FOR AN IFR CLRNC. BEING 'WITH HER' DOES NOT GIVE US THE ABILITY TO FLY IFR. ONLY AN IFR CLRNC CAN DO THAT. IN THE LAST 6 OR 7 MONTHS; WE HAVE SEEN THIS SIT HAPPEN MORE OFTEN WITH ZKC; ESPECIALLY ON WKENDS. WE HAVE TO WORK WITH THEM A LOT AND FOR THE MOST PART; THEY ARE JUST GREAT TO WORK WITH AND I SINCERELY APPRECIATE THEM. HOWEVER; I AM CONCERNED THAT THE CTLRS; EITHER BY ACCIDENT OR BY JUST NOT KNOWING REGS; ARE GOING TO PUT US INTO A SIT WHERE WE MAY BE VIOLATED BECAUSE THEY THINK WE ARE OPERATING CONTRARY TO AN ATC CLRNC; OR WORSE; PUT US OR SOMEONE ELSE IN DANGER OF AN ACCIDENT.