Matt--
There is a bona fide sand ridge that runs north to south through a sizable part of Florida, which means that a lot of the exposed sand on the courses you mention is native. Holes built directly on that structure (whose nature I believe has been discussed here a little bit in the past) drain quite well, such that such holes, even on public courses, tend to have non-continuous cart paths. I played a course called The Habitat (Bolly Horschel grew up playing there) once, whose back nine is built on the sand ridge, at the end of a month of torrential rains, and those holes were basically bone-dry.
Indeed, the county facility where I play golf here in Vero Beach (Indian River County) is called Sandridge Golf Club. This feature lends some intrigue to the terrain of a number of courses - even those pretty close to the coast - 'round these parts.