That isn't necessarily true in NY State. This is from the NYS Vehicle and Traffic law:

Section 1234. Riding on roadways, shoulders, bicycle lanes and bicycle paths.

(a) Upon all roadways, any bicycle shall be driven either on a usable bicycle lane or, if a usable bicycle lane has not been provided, near the right-hand curb or edge of the roadway or upon a usable right- hand shoulder in such a manner as to prevent undue interference with the flow of traffic except when preparing for a left turn or when reasonably necessary to avoid conditions that would make it unsafe to continue along near the right-hand curb or edge. Conditions to be taken into consideration include, but are not limited to, fixed or moving objects, vehicles, bicycles, pedestrians, animals, surface hazards or traffic lanes too narrow for a bicycle and a vehicle to travel safely side-by-side within the lane.

http://www.nysgtsc.state.ny.us/bike-vt.htm#sec1234

In the end though, I'm going to ride where I feel safe, not where someone thinks I should ride.