I had to admit that my cultural bias would have otherwise not allowed such a thought to cross my mind. "Park" and "private" simply wouldn't connect :) In countries I have lived in before Japan, it's the businesses that would have to buy land from the government - parks are automatically public. So it's totally different logic. But yeah, makes sense I guess - once upon a time people owned that land, it became expensive, and now in order to own it local governments need to buy it.
Well, as long as it increases the number of parks in Tokyo, I'll learn the new concept of private park and use it :) I just hope that there will always be enough social pressure for the owners to keep the parks.