Parse it any way that you desire, but that is the way it works in many cases. My home club leases land located inside a county park. The check goes to the parks department. We have exclusive use on weekdays, and we open the field to any AMA member on weekends (they pay a day use fee). But, we still control the field and as such require AMA membership to fly there. Nobody gets hung up if it is still a "park" or "leased public land". However, it is STILL located in the park, on the land designated by the county as park land, and it is patrolled by the park ranger.

But I am sure you are right, it is not a park anymore.