This is an interesting case in what it actually means to own something. In case you're interested, here's more on adverse possession from Wikipedia:
Adverse possession is a process by which premises can change ownership. It is a common law concept concerning the title to real property (land and the fixed structures built upon it). By adverse possession, title to another's real property can be acquired without compensation, by holding the property in a manner that conflicts with the true owner's rights for a specified period. For example, squatter's rights are a specific form of adverse possession.