DC9 FLC INITIATE AN EVASIVE CLB IN LIEU OF VECTORS DUE TO ZOB ISSUED TFC. PIC QUESTIONS CTLR HDGS TO CLR TFC.

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WHILE FLYING ACR CMH-DTW; INBOUND ON DTW 147 DEG RADIAL AT 12000 FT; I WAS ADVISED OF VFR TFC AT 10 O'CLOCK POS; 10 MI; SAME ALT. ZOB THEN ADVISED 'TFC 11 O'CLOCK POS; 5 MI; TURN L 30 DEGS.' AT THIS POINT I OBTAINED VISUAL CONTACT WITH THE ACFT. WE APPEARED TO BE HEADED DIRECTLY AT EACH OTHER. ZOB THEN COMMANDED A FURTHER L TURN TO 270 DEGS. AT THIS POINT IT WAS APPARENT TO ME THAT A MIDAIR COLLISION WAS POSSIBLE; AND RATHER THAN TURN BELLY-UP TO THE ACFT; I ELECTED TO KEEP HIM IN SIGHT AND CLB 500 FT. WHILE AT 12500 FT THE VFR ACFT PASSED DIRECTLY BELOW ME AT 12000 FT. THE TCASII DID NOT ACTIVATE UNTIL HE HAD PASSED AND I WAS RETURNING TO MY ASSIGNED ALT. WITHOUT VISUAL SIGHTING; THIS COULD HAVE BEEN A MUCH MORE SERIOUS EVENT. THE ATC CTLR FAILED TO RECOGNIZE THE SERIOUSNESS OF THE SIT IN A TIMELY MANNER; AND WHEN HE DID; HE ATTEMPTED TO TURN US INTO THE PATH OF THE ONCOMING ACFT WITH INSUFFICIENT TIME TO AVOID A COLLISION. I FELT THAT MY RADIUS OF TURN AT THAT SPD WAS INSUFFICIENT TO CLR HIS PATH; SO I ELECTED TO CLB 500 FT. HAD THIS SIT OCCURRED IN WX OR HAD I NOT SEEN HIM VISUALLY; THIS COULD HAVE BEEN A VERY SERIOUS INCIDENT. I BELIEVE THE ATC CTLR MADE AN INCORRECT ATTEMPT TO SEPARATE THE ACFT AFTER WAITING TOO LONG TO RECOGNIZE THE DANGER. I ALSO AM CURIOUS WHY A VFR ACFT WAS FLYING AT 12000 FT THROUGH THE DETROIT ARR CORRIDOR.