It sounds almost like you’re doubting the word of a real life policeman. How unamerican. America was built on the backs of our police. Imagine the dystopia we’d live in, had Tulsa not been saved.
I have a 750w inverter plugged into my 12v plug, and it is absolutely more than enough to run the little 500w single plate burner I have.
I have used them together but I don't do it outside of camping when it's too rainy to use a fire. It takes forever to cook bacon eggs and pancakes on a single burner.
You can buy portable frying pans that run on the 12V AUX power, about 180W. They get it hot enough to burn things. Although it takes 10-20min for it to reach that temperature, even with the lid on. And you can't just keep frying a bunch of things without letting it reheat.
I have a portable battery station (BLUETTI) that can plug into a cigarette outlet and it can power 3,000w of cooking things. Maybe that part could have been left out of the story.