(a) The board has no jurisdiction over a public beach located inside the boundaries of the county that has been designated a national park, national seashore, or state park.
(b) The authority of the board preempts the right of the county board of park commissioners to act with regard to a beach, park, or facility within the jurisdiction of the board.
(c) The provisions of this chapter are cumulative of other laws relating to county parks but take precedence in the event of conflict.