Now my first thought is that the radio waves applied, while similar to electricity but enough different, are not enough to break the molecular bonds of hydrogen and oxygen found in plain water. Note that it only works with salt water and what does salt water have in it that regular water does not? Salt. Mostly sodium chloride or NaCl. Sodium burns, and unless they have spectrometized teh flame to verify taht it is hydrogen burning my guess is taht it is teh sodium instead.
But the sodium is already oxidized by chlorine. Ionized by it, in fact. You think a little old oxygen molecule is going to make a chloride ion give its electrons back to the sodium ion so it can take them for itself? Now that would take some real persuasion!
But the case for burning hydrogen is almost as weak. Like the sodium, it's already oxidized. How do you burn something that's already burnt? (Yeah, I know. Use a roach clip.) The thing is, hydrolysis of water to yield oxygen and hydrogen takes as much energy as you get back from burning hydrogen (i.e. combining it with oxygen) to get water. That's at the atomic level. In reality you lose energy because of the second law of thermodynamics.
I notice they didn't say anything about comparing the input and output of energy, but if they're actually expending enough energy to cause partial hydrolysis, that's way more than the re-oxidation is yielding. For one thing you have to consider that most of the radio waves are going off into space--even the majority of the radiation directed at the test tube. You have to remember that matter is mostly empty space, so the odds of any given photon hitting a water molecule are just staggeringly small.
I'm going to go way out on a limb here, but I think this story is