You also need to put that TV episode into context. They were in the jungle for an extended period of time without protection. They were probably getting a few hundred bites a day easily and without end. Now to extrapolate a rain forest jungle with a mosquito population density probably 1000 fold greater than St Martin and that most travelers to St Martin are generally in environs for most of their stay where there are no mosquitoes (beaches, bedrooms, air conditioned rooms) then the risk of acquiring dengue/chikungunya is extremely low. We are probably talking about an incidence rate for travelers of about 1:10,000 to 1:50,000. So I don't think it is particularly fair to compare a tropical rain forest with the developed environs of St Martin.
Going back a few years, we were all paranoid when the Dengue epidemic broke out 5 years ago and peaked 2 years ago. There are select war stories out there about the misery the short term viral illness caused but just like influenza, they all fully recovered (unless they had increased risk due to underlying medical conditions or secondary exposures.) I am quite sure that the same exagarated risk assessment or hysteria will ensue here.
For further evidence about media fueled hysteria where our clinics in the states went through this with H1N1 2 years ago if you recall. That virus actually was scarier and considerably more virulent than this one would be because of the mortality rate among healthy young adults. But that virus came no where close to the hysteria that preceded it. Here are the basic facts: 1. It will be exceptionally rare that travelers acquire this disease even if it becomes an epidemic because of their transient presence on St Martin. 2. If acquired, it is a recoverable and treatable viral infection. It is not a fatal or permanently harming viral infection. 3. Sugar, alcohol and tobacco pose much greater risks and consequences to our health than this virus will.
Now that you are armed with that information. You can decide what to do.