Actually the websites for these closed areas are explicit on how to treat these areas. I tried to put the following in the description, but maybe I missed one of the areas.
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This is a closed area. Entering a closed area is punishable as an infraction or a misdemeanor according to https://www.openspace.org/trail-use-regulations.
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It sounds like what you're really saying is that the the protect_class and boundary=protected_area are the important and sufficient values, and that leisure=nature_reserve shouldn't be used because they're marked as closed areas on the Open Space District website. From what I saw, that's insufficient to classify what the area is supposed to be used for, and that the access=no/private adequately classifies who can access such areas.

With that being said, I think there may have been some confusion. One of the areas that I touched is managed by the Open Space Authority of Santa Clara Valley and not the Midpeninsula Regional Open Space District. I'd like to make sure that we're talking about the same areas and aligning with what we're reading from the websites. Can you point at which areas of concern that you want modified?