In Minnesota the law says if it's on public land, it's a public stand. If the guy that hung the stand comes out and sees you in it, the most he can do is politely ask you to hunt somewhere else. Of course I'm not going to intentionally push someone out of their own stand but if it's vacant and I want a place to sit, I'm climbing up. In one of the areas I hunt I don't bother to hang my own stand as there are enough 'public stands' that only get sat in on weekends. Not sure what the law says in NY but I'd hunt the hell out of the area you describe, especially mid-week.