MD80 CREW RESPONDS TO TCASII RA AFTER BEING CLRED TO ALT IN CONFLICT WITH OTHER TFC IN ZID AIRSPACE.

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LEVEL AT FL310; CHKED IN WITH ZID LEVEL FL310. WE HAD LIGHT CHOP/TURB AND HAD A JOLT OF MODERATE TURB. I REQUESTED RIDE RPT. WAS TOLD FL280 HAD BETTER RIDE. REQUESTED FL280. STOOD BY AND WAS CLRED TO DSND TO FL280; TURN L 180 DEGS FOR IN-TRAIL SPACING TO DFW FOLLOWING MD90. AS WE CAME ONTO 180 DEG HDG; RECEIVED TA. SAW MD90 AT 1200 FT; APPARENTLY LEVEL AT FL280. FO WAS FLYING AND HE REMARKED ABOUT WHY THEY WOULD TURN US INTO TFC. THEN RECEIVED RA OF CLB. FO DISCONNECTED AUTOPLT AND BEGAN CLB. RECEIVED RA AT FL287. AT THAT TIME ATC CALLED AND ASKED WHAT ALT WE WERE GOING TO AND I ADVISED FL280. DIDN'T TELL HIM YET WE WERE RESPONDING TO RA. HE SAID WE WERE ONLY CLRED TO FL290; CLB NOW. WE WERE BACK TO FL290 AT THIS TIME AND THE MD90 CREW CAME ON FREQ AND WANTED TO KNOW WHAT WE WERE DOING. ATC THEN TOLD US TO CALL WHEN ON GND. WE HAD USED THE POINT AND SHOOT -- I READ BACK CLRED TO FL280; POINTED AND FO VERIFIED. WE WERE PERPLEXED AT THE FL290. NEITHER ONE OF US HAD HEARD THAT RESTR. I CALLED ZID AND SPOKE WITH AREA SUPVR AND HE SAID IT HAD BEEN THEIR ERROR; WE HAD BEEN CLRED TO FL280 AND ACKNOWLEDGED FL280. THEY HAD PULLED THE TAPES AND VERIFIED THIS.