2 SINGLE ENG HIGH WINGED ACFT; ONE DEPARTING AND ONE ARRIVING; HAD AN NMAC NEAR DTO. THE ARRIVING ACFT INCORRECTLY RPTED ITS POS.

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I HAD JUST DEPARTED DTO; VIA A L TURNOUT AND DOWNWIND DEP OFF RWY 35. AS I CLBED SBOUND; I LISTENED AS A PLT MADE CONTACT WITH DTO. THIS ACFT STATED HE WAS SE OF THE FIELD INBOUND. MY DEP CLRNC WAS TO THE SSW BACK TO MY HOME-FIELD. AS I CONTINUED TO CLB; TWR ADVISED THE CONFLICT TFC THAT HE DID NOT HAVE HIM IN SIGHT. THE CONFLICT TFC REITERATED HIS POS; SE. THE CONFLICT OCCURRED AS I WAS PASSING THROUGH 2000 FT MSL; APPROX 5 MI SSW OF THE FIELD. THE CONFLICT TFC WAS DIRECTLY AT MY 1 O'CLOCK POS HIGH; HDG IN THE DIRECT OPPOSITE DIRECTION APPROX 100 FT IN FRONT OF ME AND 100 FT ABOVE ME. I WAS CLOSE ENOUGH TO NOTICE THE PAINT SCHEME OF THE ACFT. EVASIVE ACTION WAS TAKEN BY BRISKLY PUSHING FORWARD ON THE YOKE TO ARREST MY CLB AND BRIEFLY DSND. THE CONFLICTING TFC ACCIDENTALLY KEYED HIS MIKE AND WHAT WAS HEARD IN AN ELEVATED TONE WAS 'I GOT HIM.' AS THE CONFLICTING TFC MADE THIS ANNOUNCEMENT; HE MUST HAVE REALIZED HE WAS SW OF THE FIELD; NOT SE OF THE FIELD; BECAUSE HE IMMEDIATELY ADVISED TWR HE WAS SW OF THE FIELD. AS THIS XMISSION ENDED TWR ADVISED THE CONFLICTING TFC THAT I WAS SWBOUND IN HIS VICINITY. I WAS CLRING THE DELTA AIRSPACE AT DENTON AND REQUESTED FREQ CHANGE WITH NO FURTHER COM TO THE TWR. I FEEL THE PROB TO THIS SAFETY INFRACTION WAS DUE TO THE FACT THE CONFLICTING TFC INACCURATELY RPTED HIS POS ON SEVERAL OCCASIONS AND IN DOING SO CAUSED A CLOSE TFC CONFLICT. SOLUTIONS TO THE PROB WOULD BE RADAR SVCS AT DTO; A VERY BUSY GA ARPT. I WAS VIGILANTLY SCANNING THE SKIES WITH A 'SEE AND AVOID' MENTALITY AS ALWAYS. THIS WAS TOO CLOSE; TOO LATE FOR MY COMFORT ZONE. THE TWR WAS ALSO VIGILANT AND ADVISED THE CONFLICTING TFC OF MY LOCATION ONCE THE CONFLICT TFC POSITIVELY IDENTED HIS LOCATION.