MCI APCH ISSUES TFC ALERT AND TURNS A BE40; WHAT THE FLC DETERMINES AS A GREATER POTENTIAL FOR CONFLICT; AND TURNS THE OPPOSITE DIRECTION.

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ARRIVING INTO THE KANSAS TERMINAL AREA VIA THE TYGER 4 ARRIVAL; OUR ACFT WAS TURNED OVER TO KANSAS APCH CTL PASSING TRIKE INTERSECTION. WE WERE GIVEN A COUPLE OF STEP DOWN ALTITUDES AND TOLD TO FLY A 330 DEG HEADING. DESCENDING OUT OF 6000 FT TO 4000 FT APPROX 15 MI FROM THE MKC ARPT; WE CALLED THE ARPT IN SIGHT. THE CTLR TOLD US TO MAINTAIN 3000 FT BUT DID NOT CLR US FOR A VISUAL APCH. WE AGAIN CALLED THE ARPT IN SIGHT AND DESCENDED TO 3000 FT. APPROX 5 MI FROM THE ARPT; STILL AT 3000 FT; THE CTLR CALLED US AND SAID HE HAD A TFC ALERT; TURN LEFT TO 280 DEG IMMEDIATELY WE HAD TFC AT 12 O'CLOCK; LESS THAN A MILE SAME ALTITUDE. MY CO-PLT AND I SAW THE C210 AT THE SAME TIME AND BOTH AGREED A 280 DEG HEADING WOULD PUT US RIGHT ACROSS THE FRONT OF THIS ACFT. WE TURNED TO THE RIGHT INSTEAD. THE OTHER ACFT PASSED OFF OUR LEFT SIDE APPROX 1/8 OR A MILE OF LESS. AT THIS POINT WE WERE LESS THAN 4 MI FROM MKC AND THE CTLR ASKED US IF WE HAD THE ARPT IN SIGHT. WE TOLD HIM WE HAD TOLD HIM TWICE THAT THE ARPT WAS IN SIGHT AND THE TFC HE CALLED OUT WAS PASSING OFF OF OUR LEFT SIDE. HE RESPONDED BY SAYING THAT HE WAS A LITTLE BUSY AND THE FREQ WAS CONGESTED. HE AT THAT POINT CLEARED US FOR THE VISUAL APCH TO RWY 1 AT MKC. MYSELF AND MY CO-PLT BOTH FEEL THAT HAD WE MADE THAT TURN TO 280 DEG WE WOULD HAVE COME VERY CLOSE TO A MIDAIR WITH THE C210. WE FEEL THE CTLR WAS OVERWHELMED AT THE TIME AND MADE A MISTAKE BY REQUESTING THE TURN TO 280 DEG WHICH IS WHY WE MADE OUR TURN TO THE RIGHT.