There have been many cases, too numerous to count, that have defined what is and is not private property within the meaning of certain laws. A public parking lot would not meet that definition in 626.9, which is why Theseus was convicted. He was not allowed to even present the private property defense, because prior cases had gutted that section of the law. It may be written on paper, but it's entirely worthless. Just forget about the whole concept of private property within the borders of California. About the only place left that has any semblance of "private" left would be the inside of your locked home or business, or within the fenced (and gated) portion of your yard or acreage. They'll get around to taking that away, too, eventually.