Yes, they would apply. Apparently I am completely wrong here as common sense doesn't come into play in the definition of public vs. private here..
According to FL Dept of Health and FL Statutes:.
FL Statutes 514.011 Definitions.—As used in this chapter:
(1) “Department” means the Department of Health.
(2) “Public swimming pool” or “public pool” means a watertight structure of concrete, masonry, or other approved materials which is located either indoors or outdoors, used for bathing or swimming by humans, and filled with a filtered and disinfected water supply, together with buildings, appurtenances, and equipment used in connection therewith. A public swimming pool or public pool shall mean a conventional pool, spa-type pool, wading pool, special purpose pool, or water recreation attraction, to which admission may be gained with or without payment of a fee and includes, but is not limited to, pools operated by or serving camps, churches, cities, counties, day care centers, group home facilities for eight or more clients, health spas, institutions, parks, state agencies, schools, subdivisions, or the cooperative living-type projects of five or more living units, such as apartments, boardinghouses, hotels, mobile home parks, motels, recreational vehicle parks, and townhouses.
(3) “Private pool” means a facility used only by an individual, family, or living unit members and their guests which does not serve any type of cooperative housing or joint tenancy of five or more living units.
The Florida Department of Health enforces regulations on public swimming pools. While community association pools are generally not open to the public, they are considered ""public pools"" for the purpose of compliance with Chapter 514 of the Florida Statutes and Rule 64E-9 of the Florida Administrative Code.
The Florida Administrative Code defines a "public pool" as basically any pool that does not qualify as a private pool.
I apologize for any confusion as a privately owned pool, not owned by the local govt, doesn't seem to me to be "public".