in any case it depends, people tend to mark things as private despite the road not really being private, they dont want people there... as witnessed by some people putting fake signs on public forests.  this is definitely a different case but the problem still exists.
btw it takes a few days for graphhopper, osrm, valhalla, etc. to propagate changes, and unknown for other routers (like my garmin...can takes months for me to generate gmapsupp for it and reflect the change...)