I am not a legal scholar, but anecdotally a common theme in US law is that if you don't make obvious attempts to stop someone from doing something with your property (be it land, objects or intellectual property) then you are tacitly approving it.

The most well known example is probably Trademark Erosion.

Given this theme, it's not hard to see how a judge could rule that if you allow a lot of people to traverse your land, you are inherently maintaining a passageway and are thus responsible for ensuring its safety.