True, but there's no law saying we can't fight emotion with emotion.
If they persist in stating false statistics, I counter with, "That's a lie." Not "that's not true," or "that isn't the case." I use "That's a lie." If they object, then state that if you persist in saying something that reality and experience contradict, then you're either ignorant or you're telling a lie - so which is it?
Raise the fundamental moral issue of self-defense - a concept that they are completely unwilling to face. I expose their cowardice and moral bankruptcy for what it is. That's their worst nightmare.
The idea is to put the irrational 'arguer' into a position where they're obliged to defend their position - a position that we all know is morally and logically indefensible.