You don’t pour water on a grease fire because grease floats and it will spill out of your pot and catch the rest of your kitchen on fire

I expect you know as you were mainly talking about batteries (on this post about batteries) - but grease fires are not quite dangerous just because grease floats and adding water causes it to spill fire - when you introduce the water it does sink, but then it superheats to vapour, rapidly expanding and almost erupts the oil, chucking a poor man's napalm round everything in the vicinity

It doesn't have to even be on fire, if the oil is >100 degrees and there's enough of it to superheat adding water will do the same thing (minus the flames) - a melted face is better than a melted face and a house fire, but neither are recommended