In the states that I've been a resident, you have no legal right to pursue or retrieve a game animal from someone else's property without permission. If you do, you are trespassing and subject to prosecution.
From my point of view, if someone politely asks me for permission, I'll most likely say yes, and help them retrieve their animal.
I expect the same courtesy from someone else that I would give if I were in their shoes. I sometimes hunt small parcels and I've lost a deer because the neighbors didn't want me entering their swamp. I wasn't thrilled, but I understood. I wouldn't want anyone stomping through any of my sanctuary areas either.
If someone just comes marching through my property without permission (where I'm likely to be hunting), the game Warden is getting a call and tickets will be issued. I spend too much time, effort, and money on land management for my hunting to let anyone come traipsing through randomly. Their failure to put the animal on the ground on their own property does not give them the right to enter my property without my express permission.
I'd like to know more about this NY law that allows you to retrieve game animals without landowner permission. How do you proove that you are retrieving and not pursuing? A three legged, gut-shot BOAL can leave a visible blood trail and still not be fatally hit...