That is a definite, yes. 
Commercial airplanes do not necessarily fly directly over Manhattan (but do sometimes) when landing or taking off at JFK and LGA in general (as landing patterns either follow a Hudson or East River path), planes are already at an altitude of 1200’ 5 miles from the airport when landing. This is why Brooklyn and Queens have relatively low skylines, more so due to LGA than JFK. I don’t believe EWR planes ever really fly into NYC airspace, the planes actually even fly west of Staten Island.
I’m sure the FAA imposes those height restriction in the case that a plane does need to make an emergency landing when it can not follow a designated flight path. But I am not aware nor in the zoning does it explicitly mention a set height, it just all involves a lot of calculations from the approach of the runways end.