ATX LTT QUESTIONED ABORT TURN BEING MADE WHILE IN COMPLIANCE WITH SAN SID.

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CLRNC DELIVERY GAVE CLRNC AS AFTER TKOF HDG 275 DEGS TO BOARDER 2 DEP; JULIAN TRANSITION; THEN AS FILED. ON TKOF TWR SAID; 'CLR FOR TKOF; HDG 275 DEGS.' BOARDER 2 RWY 27 IS ATTACHED (SEE ATTACHED). AFTER TKOF I STEERED 275 DEGS UNTIL REACHING TUFFI INTXN; THEN TURNED LEFT TO 120 DEGS; ABOUT 20-25 DEGS INTO THE TURN ATC SAID; 'TURN LEFT TO 180 DEGS;' AND WE ACKNOWLEDGED. THEN ATC ASKED IF WE HAD STARTED TURNING BEFORE THEY GAVE US THE TURN. I REPLIED IN THE AFFIRMATIVE FOR BOARDER 2 DEP. THEY SAID THAT THE TWR TOLD US TO MAINTAIN 275 DEGS (THEY DID NOT). THE PROB THAT I SEE HERE IS THAT THE TWR DID NOT TELL US TO MAINTAIN 275 DEGS AND IN THE BEGINNING CLRNC DELIVER; IF THEY WANTED US TO MAINTAIN 275 DEGS (AS I UNDERSTAND IT) SHOULD HAVE SAID; 'AFTER TKOF HDG 275 DEGS FOR RADAR VECTORS TO THE BOARDER 2 DEP;' WHICH THEY DID NOT. AS THE BOARDER 2 CLEARLY STATES; I AM TO TURN LEFT TO 120 DEGS UNLESS TOLD TO MAINTAIN A HDG OR ADVISED BY CLRNC THAT I'M GETTING RADAR VECTORS TO THE DEP IN PROGRESS AT SOME OTHER POINT THAN AS PUBLISHED.