I didn't see the TV commercial, so my comments are general.
Oil additives already in oil are detergents, dispersants, anti-wear, friction modifiers, and anti-oxidants. Of these, one could add more friction modifiers, which would make the boundary lubrication conditions less stick-slip, and consequently some of the energy consumed to overcome this friction is available at the crankshaft. Fuel economy benefits from lubricant friction modifiers can be up to a few percent.
To reduce the bulk oil temperature, in my experience, this has only happened when reducing the viscosity (noticeable when converting from SAE 50 to SAE 20W50, for instance.) The shear in a thick oil generates a great deal of heat in the oil. The specific locations in an engine that generate heat from boundary lubrication conditions (and that are benefitted from friction modifiers) are not plentiful enough to show a significant change in bulk oil temperature. (If it did see a temp change from FM, you would have been on the way to wearing out the engine.)
Some "quack" oil additives were old technology gear oil additives that relied on certain metallurgy in the ring and pinion gears. This chemistry was extremely aggressive and could damage (corrosion) internal engine parts.
Fuel additives are generally various types of detergents that clean parts and restore performance. I'll say that again; you are getting back the power the engine had, but that was taken away when deposits formed. Cleaning up an engine changes the power output, but only back to where it should have been.
There are also fuel additive friction modifiers. These additives reduce friction above the ring travel, where the lubricant doesn't easily get to. They are quite a special class, since it provides a "lubricant" performance function but must be compatible with fuel and intake systems. Data to support a few percent fuel economy improvement exists.
From my prior life in the chemical company of an large oil company, I can believe combinations of lubricant, lubricant additive boosts, and fuel additives can change fuel economy by 5%. In fuel economy testing, it is a large task, but eventually you can keep everything constant (oil temperatures, engine speeds, vehicle transmission/differential temperatures, ambient temps, etc, etc) and accurately measure changes in fuel consumption due to the change you're interested in.
I never got the chance to use the same combinations to measure power output, which is a far greater challenge. Most dyno pulls are from low to high RPM, coolant temps are changing, oil temps are changing, etc, etc. For example, if you started with a 20W50 oil, as it heated up from pull to pull, it would warm up and thin out. Power would go up. What would be a better experiment is to go back to the original conditions (i.e. without the additive) and see if the power went back down. Of course you can't then take the additive out of the oil, so you can start to see how you have to be clever when trying to make these assessments. Again, I didn't see the show, so I can't comment on their test procedure. But I think there are combinations of additive components that, but reducing friction, allow greater flywheel output.
