That's not how I understand it. You may be referring to some other use I am not aware of. I'm not a car guy.

"A nitrous oxide engine is an internal combustion engine in which oxygen for burning the fuel comes from the decomposition of nitrous oxide, N2O, rather than air. The system increases the engine's power output by allowing fuel to be burned at a higher-than-normal rate, because of the higher partial pressure of oxygen injected with the fuel mixture."

https://en.wikipedia.org/wiki/Nitrous_oxide_engine

Supercharged usually refers to an engine with a supercharger, which is a crankshaft driven pump used to force more air into the engine. It is similar to a turbocharger, except a turbo is driven by exhaust gas.

N2O is typically used with a normally aspirated gasoline engine. It's just another way to get more oxygen into the combustion chamber.

https://www.racingjunk.com/news/drag-race-101-its-a-gas/

You can absolutely run N2O with a turbo or supercharged engine. I ran a NXExpress rig on my '99 Eclipse GSX back in the day (with a big turbo).

They didn't say it couldn't be used with a super charger, they said it wasn't exclusively used with a super charger.

This same effect can be accomplished by spraying cold water into the air inlet, and this is used in some high end cars and jet engines. It also cools hot points in the engine, letting you push the compression higher without causing premature detonation.

Does mean you have to refill a water tank too, but it also lets you get more power without producing any more NOx, which are bad for both the environment and people.

It is a nice complement, as compressed air from a turbo or super charger is very hot. The nitrous cools it down. People also use a water or alcohol spray for a similar reason.

While it will be cooler, it also reacts better than O2 from the air. Especially since you’re injecting 100% N2O instead of 79% inert atmospheric air.

The nitrous itself also has more oxygen in it than air does.