In some cases, deeds do show the sandy beach (to the mean high water mark) being owned privately. However, there are some county restrictions about obstructions on the beach interfering with emergency and maintenance vehicles, so a sign placed in the wrong place, may not be allowed. There are also Federal laws about harming endangered species, so there could also be a problem when Sea Turtles come ashore to nest, if they are trapped by a sign.
On the flip side, private property laws state that you must defend your property, or otherwise, some of the rights could be lost in the way of easements, and other things. One way of "defending" your property is by erecting "no trespassing" signs, alerting others that it is private. The kicker in most of these newly seen signs (as in the last several years), is that we only recently began seeing them erected, and the public has been using that property for many years as though it were public, hence the debate of whether or not it has public use, even though it is privately deeded. In other words, it may be way too late to start claiming it by posting signs, more than twenty years (defined in previous cases by the FL State Supreme Court) after the public has been using it.