AHH STUPID computer, I had a hugely long well written answer for you guys and then my computer crashes...OMG I hate this thing. I really don't have time to write all that I did now so lets just REALLY compact this.
If you burn hydrogen, even just a 1 of the 2 parts needed to make water when combined with a single oxygen atom obviously a water molecule cannot be made due to the lack of sufficient hydrogen. And as far as the regular fuel being in a sufficient state that is the purpose of the electrical current being run through the water with the catalyst. This breaks it down till you have oygen, and hydrogen. period, they're done, its broken down to its fundamental state. There is no energy used to recombine the molecules because the hydrogen combusts along with the fuel. Really all the hydrogen is doing is causing your gasoline to burn more completely which then gives you better gas mileage due to the lesser amount of gasoline needed to run the vehicle.
Ah good question. Combustion itself can be done with not only gasoline but many other compounds, and is therefore a physical process since there is no single chemical reaction used in the explosion BUT there are several chemical processes done in the physical reaction of combustion such as the gasoline converting itself to co2 emissions and others. Electrolysis is pretty much self-explanatory though, in chemistry and, manufacturing btw, electrolysis is a method of separating chemically bonded elements and compounds by passing an electrical current through them. To see this for yourself try passing direct current from a battery or other DC power supply through a cup of water, I will say again however you will need some baking soda or other catalyst otherwise you will be very bored. Obviously this is not the more complex system used to make this achievable in a vehicle, but it does demonstrate the effects of electrolysis.
Finally to define chemistry..chemistry is the study of the chemical world and its application in our lives. Now I'll ask how that is relevant to this discussion? And if you really don't know what chemistry is what are you doing arguing your case about this?
And no, your right pete just to send a current through water will not break the molecules down speedily enough for it to be worth it BUT AGAIN that is where a simple catalyst of baking soda or whatever else would work certainly makes up for it.
As for this guy's report..I'm not sure why he expects there to be an automatic adjust right when he first starts it..and if you read this article here,
http://www.popularmechanics.com/automotive/new_cars/4276771.html?series=19, that guys "analysis" is pretty much blown out of the water. Obviously it can be done and oh, a car company did try it and guess what, it worked

Another thing is that guy never displayed any results, any diagrams, nothing..he didn't even reveal what kinda car he had. All he did was put a picture of the unit up which was taken while it was sitting on the ground..and if thats where it stayed well DUH of course he didn't get any results. Seems very fishy to me.