It's only a public asset as long as it's untouched (i.e. not paved or developed). The Greenbelt laws keep it that way.

Think of the Rocky Mountains as a public asset. I don't know who owns them, but that doesn't matter. They are a public asset as long as they exist, but if someone is allowed to flatten them, or carve the faces of dead prime ministers into them, they are no longer an asset to the public. Both of those are much more difficult to do than it is to build a house or a parking lot, so I'm not terribly worried about that scenario unfolding, but it's the same idea, just bigger.