I think you guys are reading too much into this...we always said it was never a good idea to be out on the beach alone in NY...defined as have some friends with you if you are the only camper on the beach, or if you are by yourself, it's a good idea to have other campers on the beach.
NOT a crime safety issue at all, nobody was afraid of being mugged, but there was a real possibility of getting stuck in the sand. If you had equipment trouble, it was miles to walk into town when the ranger station was closed during the off season. A broken valve stem when airing up could strand you if you didn't have a spare. A dead battery could leave you in harm's way of the incoming tide.
Also a general safety issue....a slip and fall and broken leg could be deadly if you couldn't get help. There's no calling 911 or ERS, they are not equipped to get out into the sand where you are.