Of course when you use energy from the alternator to separate HHO, then burn it in the cylinder, you are not getting any energy boost from the HHO. The leading theory (with some science to back it up) is the efficiency boost comes from more efficiently combusting the combined fuel in the cylinder. But my understanding is this only explains a small percentage in gain.
I have a feeling that what we are seeing is the same thing that makes hybrid engines more efficient. I think we are re-capturing some of the energy that is otherwise wasted, and recycling it. When en engine idles, when you are going downhill etc. Not all of the energy expended in running the engine is converted to movement of the car- and since the HHO system is constantly capturing a portion of the engine's output it captures some of that wasted energy as well.
Has this idea been explored? It seems to fit the levels of MPG improvement reported in the testimonials- they seem to be consistent with hybrid improvements.