Private roads can be misleading. Out here it's really just referring to who maintains it, not who can control access to it, or even who built it in the first place. That road is paved with a bridge and a guard rail, fitting between just two private lots, which homeowners typically would not fund something like that just to save five minutes from having to drive around it. Odds are it was a county built and maintained road, then it was removed due to some cost cutting measure.
