I get what you're saying. I think removing them is not the worst thing in the world, especially if you've been there in person. (I have a fairly strong opinion that local mappers should have more say than distant "armchair mappers" like myself!)
One thing also to consider is that if a trail exists in reality, leaving it in OSM but tagging it correctly (access=no, informal=yes) will do more to prevent some other unsuspecting person from coming through later and re-adding them anew. Either by in-person survey or more likely, by satellite, which won't tell them that it's private.

Hope my comments aren't coming across too abrasive! Thanks again so much for your local expertise and comments in general.