EWR TWR ACCUSED COMMUTER SMT OF CAUSING A POTENTIAL CONFLICT WITH AN ACR LGT BECAUSE THE FLT CREW DID NOT FOLLOW UNPUBLISHED DEP PROC.

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DUE TO GOOD VFR CONDITIONS WE ELECTED TO UTILIZE THE GOVERNORS ISLAND DEP AT EWR. THE DEP STATES 'CLBING TURN TO THE STATUE OF LIBERTY.' WE WERE INSTRUCTED TO CLB AND MAINTAIN 1400'. WE DEPARTED RWY 29 AT EWR AND WERE INSTRUCTED 'IMMEDIATE LEFT TURN DIRECT TO THE STATUE. MAINTAIN 1400'.' THE CALL WAS ACKNOWLEDGED AND THE TURN WAS STARTED. APPROX 1 MIN LATER WE WERE INSTRUCTED 'TIGHTEN THE TURN; PROCEED OVER THE TWR CAB.' THE CALL WAS ACKNOWLEDGED AND THE BANK ANGLE WAS INCREASED FROM 25-35 DEGS. AT THE TIME THE CALL WAS ACKNOWLEDGED; WE WERE APCHING THE DEP END OF RWY 22R (THE ACTIVE RWY FOR DEPS). WE WERE LEVELING AT 1400' AND INDICATING APPROX 150K. FORESEEING A POTENTIAL CONFLICT; THE CTLR ADVISED 'ACR LGT DEPARTING 22R.' WE ADVISED TFC IN SIGHT. WE PASSED APPROX 1200' ABOVE THE LGT AND WERE THEN HANDED OFF AND GIVEN VECTORS ON COURSE. WE WERE LATER ADVISED TO CALL EWR TWR. VIA TELEPHONE; EWR TWR ACCUSED US OF NOT FOLLOWING INSTRUCTIONS AND CAUSING POTENTIAL CONFLICT. WE RESPONDED BY SAYING THAT WE HAD FOLLOWED ALL INSTRUCTIONS. IT IS MY OPINION THAT THE CTLR MISJUDGED NOT ONLY OUR SPD; BUT OUR DISTANCE FROM THE ARPT AND OUR RADIUS OF TURN. ALL OF THE ABOVE CAUSED US TO FLY OVER THE DEP END OF RWY 22R. HAD WE INITIALLY BEEN INSTRUCTED TO TURN LEFT AND PASS OVER THE TWR; A CONFLICT NEVER WOULD HAVE ARISEN. MY RECOMMENDATION IS THAT IN THE INITIAL CLRNC FOR RWY 29 GOVERNORS ISLAND; IT SHOULD BE STATED 'LEFT TURN DIRECT EWR TWR; THEN VECTORS ON COURSE.' AS THE CREW; WE NEVER PERCEIVED A POTENTIAL CONFLICT. ALL COM WAS CLR AND CONCISE AND UNDERSTOOD BY ALL PARTIES. ALL INSTRUCTIONS WERE ACKNOWLEDGED AND ACTED UPON. AT NO TIME DID WE DEVIATE FROM THE CLRNC AND/OR INSTRUCTIONS GIVEN. IN OUR OPINION IT WAS CTLR ERROR.