In order for there to be adverse possession, the adverse party must openly occupy the property exclusively and must keep others off it, and use it as if it were his own. This is called hostile possession which must be continual and - here's the very important part in the case stated - without the owner of record's challenge or PERMISSION. In this case, because the guy with the RV didn't know he was on another's property prior to being notified by the new owner, he was not a hostile possessor and, once the new owner gave him permission, pending a later mutual agreement, he could never become a hostile possessor and would not prevail under statutory adverse possession - unless the statute says otherwise this is common law. All hostile possessors are initially trespassers and can be evicted by the owner of record and are subject to arrest under local trespassing law - the theory is that the owner of a property who cares, needs to be aware of his property's condition and take action to protect his/her interests.
Easements are another matter - the way it was described, the neighbor had a right to a 20' easement regardless of the size of the actual road over which the easement was permitted. I didn't find what the outcome was except that the OP lost, but I don't know lost what.