[kqr]

I agree. Single examples of extreme weather will happen. They will be unlikely under the null hypothesis and slightly more likely under a hypothesis of global warming, but single examples are not definitive proof of any kind.

In other words, there may well be lots of good evidence that death by lightning is decreasing (there is) but "look, this year only three people died compared to 11 last year!" is definitely not sufficient on its own.

Again, death by horse kick in the Prussian army is probably a relatively constant cause, but seeing that "3 people died that way last year and this year!" is not proof.

However, maybe they are the sort of narrative that helps less statistically sophisticated people understand. You and I can get our understanding from the relatively solid science and probabilistic reasoning. Many people can't, and the only way to teach them is by example, even if that method is technically flawed.