I saw the same piece a few days ago here in Houston. Must be syndicated. Or, more likely, a PR piece from the company itself.
At any rate, I did a little googling on it.
An informative link:
http://www.phact.org/e/bgas.htm
Wikipedia's entry:
http://en.wikipedia.org/wiki/Brown's_gas
You'll notice they're a little sceptical. The documentary notes that they get their gas from a special fuel cell. Right there you can just jump straight to the assumption that they're working with a plain stoichiometric mix of hydrogen and oxygen. To suggest anything else is a huge scientific leap. Hydrogen and oxygen exist in just a few stable states at our kind of pressures and temperatures. You have water, hydrogen peroxide, and diatomic gases. You can't arrange a gas to somehow produce more energy in combustion just because of how you make it. You could make the same mixture with seperate bottles of gases and good regulators.
That said, hydroxy mixtures are useful. They've been used in "water torches" for decades. Electrolyze some water, pump out the gases through a torch, and light them. You get a nice, small, cool flame with no storage of volatile gases. They're great for jewelers that don't need much heat.
Using the gas for a car is something else again. Your choices are to generate and store the gas, or make as you go like with the torch. Storing a mixture of hydrogen and oxygen that only needs an ignition source to combust is asking for trouble. Meanwhile, if you're making it as you go, you'll need a bank of batteries and a nice heavy fuel cell. At which point you have to ask yourself why you're not just using the batteries to run a nice efficient motor instead of an inefficient combustion engine.