MD80 FLT CREW INITIATE TCASII MANEUVER DUE TO OPPOSITE DIRECTION K35A TANKER AND FIGHTER AT FL280 UNDER ZKC CTL. CTLR ERROR ADMITTED.

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WE RECEIVED A TCASII 'TFC' CALL. THE TARGET WAS 20 MI AT OUR 11 O'CLOCK POS; 500 FT BELOW; INDICATING A CLB. WE THEN RECEIVED AN 'RA' TO 'CLB.' AS WE FOLLOWED SOP'S; THE TARGET CONSTANTLY INDICATED 500 FT BELOW. WE LEVELED AT FL285 PER 'RA' COMMANDS. TFC PASSED LEVEL AT FL280; A KC135 WITH 4 F16'S IN TRAIL. THE TANKER WAS WITHIN 2 MI; THE F16'S ALL APPEARED TO BE 500 FT BELOW; AT FL280. WE RPTED THE 'RA' TO A BEWILDERED ZKC ON FREQ 132.25. CAPT ALSO SPOKE WITH MCI WATCH SUPVR AND DISPATCH. SUPPLEMENTAL INFO FROM ACN 589391: WE BEGAN LOOKING FOR THE TFC AND I WAS WAITING TO BREAK IN ON THE RADIO TO INQUIRE ABOUT IT WHEN THE TFC ALERT TURNED INTO A RESOLUTION ALERT; INITIALLY COMMANDING A 2000 FPM RATE OF CLB. WHEN CLR OF THE CONFLICT; WE RETURNED TO FL280. WHEN THE WHOLE PICTURE BECAME CLR; WE REALIZED THAT A TANKER WAS OPPOSITE DIRECTION TO US AT VIRTUALLY THE SAME ALT. I ASKED ATC IF WE WERE 'IN A REFUELING TRACK OR SOMETHING.' AFTER A SLIGHT HESITATION; THE ANSWER WAS 'ALTREV' FOLLOWED BY A TFC ALERT CALL. I ESTIMATED THE CLOSEST POINT OF PASSAGE TO BE APPROX 500 FT VERTLY AND 2-3 MI HORIZLY. THE TCASII SYS WORKED AND WE RESPONDED AS WE'VE BEEN TRAINED.