I think, for the most part, the signs you saw were to show ownershipt to prevent adverse possession. I believe the Hess property sign was put there to show that it was owned by Hess and was symbolic. My understanding is that, in times past, the property owners created an access used by the public, which benefits the property owners. However, they did not post signs indicating the property was privately owned. Doing this created a psuedo-public property right (an easesment) and, if the owners sought to shut the access point down, the government could claim it in an adverse-possession type proceedings. By posting the signs, owners are seeking to notify the public of the private nature of the property and prevent adverse possession. I do not believe the Hess’s are actually afraid of adverse-possession proceedings.