Here's how New York's DEC has it worded on their website.

Q. May a person travel in a boat or canoe on a waterway which is posted?

A. Yes, but travel may not include fishing. A person in a vessel has a right of passage on a navigable waterway, even if the bed of the waterway is privately-owned and is posted. A waterway is navigable if it is capable, in its natural state and ordinary volume of water, of transporting, in a condition fit for market, of floating logs or manufactured or agricultural goods to market. A navigable waterway need not be navigable in both directions, nor need it be navigable 12 months of the year. Furthermore, a waterway's navigability is not destroyed by rapids or other temporary obstacles so long as the rest of the waterway is otherwise navigable. Where such obstacles exist, the right to public navigation authorizes a boater to get out of the vessel and walk alongside the boat to get around such obstacles, or to portage around such obstacles, even over private property above the mean high water mark, so long as the portage is by the most direct and least intrusive safe route possible. The right to navigation does not otherwise authorize the public to go on private land above the mean high water mark, even for access to or egress from a navigable waterway. A 1997 ruling of the New York State Court of Appeals indicates that the public right to navigation does not include the right to walk on the bed of a waterway to fish, or to anchor for the purpose of fishing where the bed of the waterway is privately-owned; or to fish while navigating through privately-owned waters.