This is the SUN - a Murdoch paper, not exactly anti-US!
You have to remember who the Sun's readership is - the closest British equivalent to your "rednecks". The types who like to have a drink (or ten), hold strong (and rightist!) opinions, don't respect foreigners even when these are in their own country, and like to let off steam on holiday. On European holidays they just brawl at holiday resorts with each other, the police, the locals, no big deal.
So this is sensible advice to these readers.
Then it's doubtful that very many of them would be coming to Florida anyway. One, there's the plane fare to Florida, and two, is the fact that Disney World ain't cheap.:)