AN ACR B-757 FLEW LOWER THAN N90 EXPECTED PAST THE WORLD TRADE CTR.

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WE WERE AT 3500 FT; FLYING UP HUDSON RIVER FOR THE 'RIVER VISUAL RWY 13 LGA.' WE WERE THEN CLRED TO FLY THIS APCH. OUR APCH PLATE SPECIFIES 'REMAIN ABOVE 2000 FT AS LONG AS POSSIBLE' BUT NO OTHER ALT RESTRS. (THE 'FMS APCH RWY 13 FT SPECIFIES 3500 FT TILL CENTRAL PARK; BUT NOT THE APCH WE WERE CLRED FOR). ONCE CLRED FOR APCH; I DSNDED OUT OF 3500 FT FOR 2000 FT. PASSING APPROX 2500 FT; CTR TOLD US WE WERE NOT CLRED FOR LOWER AND TO CLB BACK TO 3500 FT. HE LATER SAID THERE WAS NO CONFLICT BUT IT WAS TOO LOW FOR AREA. IF THIS IS TRUE; THERE SHOULD BE A 3500 FT RESTR ON THE 'RIVER VISUAL RWY 13 LGA.' CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR FLIES THE B-757 FOR A MAJOR ACR. HIS COMPANY PUBLISHES AN 'FMS APCH; RWY 13' THAT IS NOT IN THE COMMERCIALLY AVAILABLE OR THE GOVT ISSUED APCH PLATES. THE COMMERCIAL AND GOVT PLATES MAKE NO MENTION OF 3500 FT ON THE RIVER VISUAL APCH. BOTH PLTS AGREED THAT; WHEN 'CLRED FOR THE RIVER VISUAL APCH;' THEY WERE CLRED DOWN TO 2000 FT. THE CAPT OF THIS TRIP CALLED N90 AFTER LNDG AND TALKED TO THE CTLR WHO AGREED THAT THERE WAS NO FORMAL RESTR. THE CTLR DIDN'T WANT THE PEOPLE IN THE EMPIRE STATE BUILDING TO BE ALARMED. MANY OF THE PAX WERE ALARMED WHEN THEY NOTICED THE ADDITION OF PWR AND THE SUDDEN CLB; ONLY TO DSND IMMEDIATELY. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: QUALITY ASSURANCE SPECIALIST STATED THE RPTR IS CORRECT. HE CAN DSND TO 2000 FT. SPECIALIST STATED NORMALLY A 3500 FT RESTR IS ADDED TO THE CLRNC TO PROTECT EWR DEPS. NO CHANGE TO THE RIVER VISUAL RWY 13 APCH IS FORTHCOMING.