You want facts, here you go.
The Villages district government site defines a CDD as follows
Community Development Districts (CDD’s) are widely used throughout the United States to provide for certain service delivery infrastructure such as water management and control (drainage), fire control, road and bridge construction and maintenance, park and recreational facilities, mosquito control, port and inlet districts, water and sewer systems, sidewalks, streetlights similar infrastructure that is required to provide urban services….
A Community Development District is a public non-profit unit of local government with the special purpose of providing the services described above. As a unit of local government, the District is subject to many of the same State Statutes that regulate cities and counties..
The multi-modal paths in TV were built along with the roads as part of the infrastructure that was paid for with federal tax free municipal bonds. Those multi-modal paths are for transportation, not recreation. You cannot use federal tax free municipal bonds to build private roadways whether they are for cars, trucks, golf carts or tricycles.
The argument that Villagers make to justify their belief that the multi-modal cart paths are private is that they are being maintained with amenity funds. Yet thousands of cities and towns across this nation have streets that are maintained with local taxes. Can you sit there with a straight face and say that those cities should then be allowed to prevent you from using those streets? Of course not. If that were allowed, the entire transportation system of this country would fall apart.