This law isn't 'obscure' where we live. It's common knowledge of all farm owners that they are responsible for the right half(when facing from your land) of a fenceline, and its upkeep. Even if you don't need it or want it. It's one of those outdated laws that was useful when folks made a living off of 80-160 acres. Most farms , when I was young, were partitioned in 10-20 acre fields.
The solution is to place the fence at least 6" inside the property line (which has to do with a law concerning surveying standards).
You will notice as you drive around Virginia that in many urban areas many lots are separated by two different kinds of fencing!
The way these folks should have dealt with this Ames character is to plan for a STRONGER fence, and then stiffed him with half the bill. Or, alternatively, immediately after construction begun "maintenance" on the fence he placed and simply send him bill after bill after bill.
It isn't at all `obscure' where I live either, digger.
In the county, to keep livestock where they belong (& to prevent such things as wandering bulls) if the neighboring 'Homer' won't voluntarily help pay for a boundary line fence a landowner can contact his township trustee. A `no-frills' field fence installed and each is billed for half the cost, which becomes a lien if neighbor won't pay. Don't wanna pay? Then don't move to the sticks to play.
Usually concluded without gunplay, however.