GV FLC CHALLENGED BY L30 CTLR WHEN FLYING THE TRAGR RNAV RWY 19 APCH WHEN L30 ASSUMED THAT THEY WERE FLYING THE RWY 25 APCH PROC.

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WE WERE ON A POSITIONING FLT FROM SJC TO LAS. I WAS THE SIC AND THE PF. WE WERE APCHING BTY VOR WHEN WE RECEIVED THE FOLLOWING CLRNC; 'AFTER BTY; CLRED FOR THE TRAGR 1; EXPECT L DOWNWIND FOR RWY 19R.' THE PNF LOADED THE TRAGR 1 AND THE RWY 19R TRANSITION; AND CHKED IT AGAINST THE APCH PLATE. WE FLEW THE ARR AS DEPICTED FOR RWY 19R; BUT WHEN WE TURNED NEBOUND; APCH CTL QUERIED US AS TO WHICH ARR WE WERE FLYING. WE REPLIED WITH THE TRAGR 1; AND WERE ISSUED A VECTOR. UPON LNDG; TWR ASKED US TO CALL APCH CTL. THE PIC MADE THE CALL AND WAS INFORMED THAT WE WERE EXPECTED TO FLY THE RWY 25L TRANSITION AS NOTED ON THE APCH PLATE. THERE IS A NOTE ON THE BOTTOM OF THE APCH PLATE THAT SAYS; 'ACFT TO PROCEED VIA LNDG RWY 25L UNLESS OTHERWISE INSTRUCTED BY ATC.' NEITHER I NOR THE PIC SAW THIS NOTE; IT IS NOT IN BOLD. HOWEVER; EVEN WITH 20/20 HINDSIGHT; WITH THE ATC CLRNC WE RECEIVED I AM NOT SURE IF I WOULD HAVE FLOWN THE ARR ANY DIFFERENTLY. THE ATC CLRNC AND APCH PLATE IS AMBIGUOUS AND CONFUSING; AND SEEMINGLY CONTRADICTORY. SINCE THIS EVENT; I HAVE ASKED QUITE A FEW FELLOW PLTS; WITH THE CLRNC WE RECEIVED HOW THEY WOULD HAVE FLOWN THE ARR.