PART 135 OPERATOR CONCERNED WITH ATC INSTRUCTIONS THAT TURNED HIS ACFT INTO ANOTHER; UNCTLED ACFT.

Narrative

DEPARTED RWY 32 AT MQY APPROX XP35 AND CLRED RWY HDG UP TO 2000 FT. IMMEDIATELY AFTER TKOF; OUR CLRNC WAS REVISED TO A R TURN TO 070 DEGS AND MAINTAIN 3000 FT. AFTER HDOF TO BNA DEP; WE (ACFT X) WERE TOLD TO MAINTAIN 3000 FT (AT THE TIME WE WERE CLBING THROUGH APPROX 2200 FT). ABOUT 1 MIN LATER; WE WERE GIVEN A TFC ALERT FOR NBOUND TFC (ACFT Y) AT 12 O'CLOCK POS; LESS THAN 1 MI; 3000 FT UNVERIFIED; AND GIVEN A HDG OF 030 DEGS. THIS L TURN WOULD HAVE CAUSED OUR IMPENDING COLLISION TO OCCUR A LITTLE FARTHER TO THE N. WITH TFC AT 12 O'CLOCK XING R TO L; THE CTLR SHOULD HAVE GIVEN US A R TURN OR A CHANGE OF ALT. I STARTED THE TURN TO 030 DEGS BEFORE I HAD VISUAL ON THE TFC. ONCE I SPOTTED THE TFC AND SAW WE WERE RAPIDLY CLOSING WITH IT; I BROKE R AND CLBED UP TO APPROX 3300 FT. THE CTLR; TOTALLY OBLIVIOUS TO HIS SCREW-UP; TOLD ME TO MAINTAIN 3000 FT. I RETURNED TO 3000 FT AND THE INITIALLY ASSIGNED HDG OF 070 DEGS. ABOUT 30 SECONDS LATER; HE ASKED FOR MY HDG AND I RESPONDED '070 DEGS.' HE TOLD ME TO FLY A HDG OF 030 DEGS AS ASSIGNED. SINCE THE CONFLICTING TFC WAS 'UNVERIFIED' AT 3000 FT; I ASSUMED HE WAS NOT CURRENTLY UNDER BNA'S CTL AND MAY HAVE BEEN A VFR ACFT AT AN INCORRECT ALT. WHILE THE OTHER ACFT WAS CERTAINLY A CONTRIBUTING FACTOR; I FEEL THAT ATC'S LATE TFC CALL AND POOR CHOICE FOR A CONFLICT RESOLUTION NEARLY CAUSED AN NMAC.