They are a public benefit corporation, and their governance is through a 21-member board. Board members are nominated by the Governor, with four recommended by New York City's mayor and one each by the county executives of Nassau, Suffolk, Westchester, Dutchess, Orange, Rockland, and Putnam counties (the members representing the latter four cast one collective vote). There are also non voting members representing unions and commuter groups.
For most purposes, they are a government agency, except for, and most especially, borrowing money. They have no taxing authority, and debt obligations of the corporation are NOT debt obligations of the state, and thus do not count against statutory limits on state borrowing, nor do they affect the bond rating of the states general obligation borrowing.
Care to elaborate? That's a pretty vague argument.
Other purpose: Their debt is not an obligation of NYS.