i don't have an issue with the language used. the distribution is the curve, or everything under the curve. it's a semantic point that a statistician would be splitting hairs over in "correcting" you on and most actually probably wouldn't bother with at all. a major hurricane hitting the united states would be a rare event, and whether you want to describe that using a "poisson distribution" or the "curve described by the poisson distribution" is just an issue in language, although i would perhaps suggest that you're misapplying the central limit theorem in a situation with not enough data points to do so, if that's what you're getting at by referencing normality. a misapplication of the clt like this could actually be used to argue for stasis. it doesn't change the point you're making.
and, yes - charting an increase in hurricanes since 2005 is kind of like charting a decrease in temperatures since 1998. or jet stream variability since 1725.
but, the important thing you pointed out was that global warming is not the only factor. and, if you want to push this on this platform, that's the most important point you can make: the universe is complicated, and this increase in carbon on this planet is just one of the things that's happening in it.