These sites are not regulated by Florida or U.S. laws, and they only have to abide by the local regulations in their jurisdictions. There is no specific law in Florida prohibiting you from gambling online by using one of these offshore sites, which will accept Florida residents. You are free to do that.
While federal law is abundantly clear on the illegality of such operations, these books and even the media, often claim it is not illegal for the consumer to use offshore sites. While it is true that no federal law targets bettors using offshore books, many states have laws that make using these books illegal.