While I do not personally know anyone who has received one, please reference the case of
Osterweil v. Bartlett. While not truly a non resident permit, the case lays out that, under NY law, a person does not need to have his/her primary residence in NY and that just owning property there and only being there part time, is sufficient to quality for a NY permit. It is believed that with this ruling, any person who owns a vacation property in NY and can prove that (i.e. utility payments, property tax payments, etc) would qualify for a NY permit.
As I stated in my first reply, a person would technically be able to obtain a NY permit. However, I would say that for all practical purposes, the application would be denied and the person would have to spend considerable time, resources, and money in the court system to, hopefully, force the offending county to follow the law as decided in the above referenced case.