As the others have said, the best practice is to map the ground truth because that is the objective of OSM, rather than cloning the council GIS.
See: https://wiki.openstreetmap.org/wiki/Ground_truth
I did the survey to specifically check whether the Waterfall Road sign was still on the pole (it is) which is why that name was reinstated by user nevw. I didn't touch any of the Frenchmens Road ways.
I understand there is no official road reserve for Waterfall Road, but still support the decision to retain the name. Generally we also do not mark ways as "private" unless they are specifically signposted as such; in this case there is no indication on the ground that any of these easements are private. As volunteers we don't go through title info for every ambiguous road reserve, of which there are plenty in the mountains. The best way to alert us to possible problems is to discuss it as here, where we can fix it quickly easily, or you can right-click the map and choose "Add a note here" with your concerns expressed clearly.