Can you clarify your concern? The iD editor shows that tag as a nature reserve, which it is, but these areas under fairly strict access conditions. So they're not open. They're closed areas.

It's my understanding that they are a part of the Midpeninsula regional open space authority and/or the Open Space Trust. They're kind of 2 sides of the same coin. Their maps show these areas as closed areas (not private areas).

To quote the OSM documentation on it (https://wiki.openstreetmap.org/wiki/Tag:leisure=nature_reserve), it says, "Such areas are reserved and managed for conservation and to provide special opportunities for study or research. Nature reserves may be designated by government institutions in some countries, or by private landowners, such as charities and research institutions." These areas meet those conditions according to the documentation.

Am I misunderstanding your request?