CAPT OF A LIFEGUARD LR25 CLBING ON RADAR VECTORS TO FL230 WAS ADVISED THAT HE WAS POSSIBLY INVOLVED IN A LTSS INCIDENT WITH AN ACR MD80 THAT DID NOT WANT TO RESPOND TO THE ARTCC RADAR CTLR'S VECTORS FOR SEPARATION. THE LR25 NEVER SAW THE ACR MD80; BUT THE M80 CLAIMED HE HAD THE LR25 IN SIGHT.

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LR25 WAS ON AN IFR FLT PLAN; LIFEGUARD FLT; DEPARTING ARLINGTON; TX (F54) ON A WORTH 7 DEP AT APPROX XA35Z; TALKING ON FREQ 127.0 DFW DEP AND FREQ 132.92 ZFW. ACR Y WAS A CONFLICT. WE HAD DEPARTED F54 AND WERE GIVEN 2 OR 3 VECTORS; THE LAST ONE BEING A HDG OF 300 DEGS TO INTERCEPT THE 262 DEG RADIAL DFW WORTH 7; TEXACO TRANSITION. WE WERE CLBING; I BELIEVE; TO 12000 FT AND AT THE TIME WE WERE TOLD OF CONFLICT WE HAD BEEN CLRED TO FL230. WE WERE STARTING OUR TURN TO INTERCEPT THE 262 DEG RADIAL AND WAS TOLD TO TURN AN ADDITIONAL 30 DEGS L FOR TFC. BEFORE WE WERE ESTABLISHED ON THAT HDG WE WERE TOLD TO TURN 30 DEGS R FOR TFC. THEN WE WERE TOLD TO FLY A HDG OF 300 DEGS; VECTOR FOR TFC. PASSING THROUGH FL190 WE WERE TOLD TO MAINTAIN FL180. WE TOLD THE CTR WE WERE PASSING THROUGH FL190 AND DID HE WANT US TO DSND AND HE SAID NO; MAINTAIN FL190. DURING ALL OF THESE VECTORS WE HEARD ACR Y BEING GIVEN 30 DEG VECTORS FOR TFC. EACH TIME THE ACR Y WAS ASKED TO TAKE A VECTOR FOR TFC; THE ACR Y; TRYING TO AVOID THE VECTOR; TOLD DEP AND/OR THE CTR THAT HE HAD US; THE LEAR JET; IN SIGHT AND COULD MAINTAIN A VISUAL. BEFORE WE LEFT THE FREQ; WE WERE TOLD WE WERE POSSIBLY PART OF A SEPARATION CONFLICT AND A PLTDEV; AND THAT IS WHY WE ARE FILING THIS RPT. WE FOLLOWED INSTRUCTIONS AND AT NO TIME HAD TO TAKE EVASIVE ACTION. WE DID NOT HEAR THE ACR Y RPT ANY EVASIVE ACTION TO THE CONTRARY; HE RPTED US IN SIGHT; AND SAID HE COULD MAINTAIN A VISUAL. WE WERE TOLD BEFORE LEAVING THE FREQ; THAT THE TAPES WERE BEING REVIEWED AND WE WOULD BE FURTHER CONTACTED IF THERE WAS A PROB. WE WERE QUESTIONED ABOUT OUR LAST HDG AND WHETHER IT WAS A HDG OR A VECTOR TO INTERCEPT A 262 DEG RADIAL OF DFW. AT NO TIME DID WE SEE THE ACR Y AND IT WAS CLR WITH 50 MI VISIBILITY. BETTER SAFE THAN SORRY.