You might think it's semantics, but cooling refers to dumping waste heat to the environment. Running rich is not chemically generating the heat in the first place, so to call it cooling is disingenuous.
Sure, it runs cooler, but it isn't cooling any more than reducing the power level is cooling.
See my post #74:
Maybe "fuel doesn't cool, it just heats less"?
So yes I agree, in part. But you could also say that cooling is "lowering the temperature" i.e. making it cooler. If you are trying to reduce your engine temperature you may not care.