Oh, you're absolutely right. I simplified immensely by aggregating at the level of a convenient political division that has only vague bearing on actual geography as well as assuming the distributions are uniform across the range in question.

I think the overall point is sound, though. A huge chunk of the US population is in territory regularly subject to strong tornadoes.

Also, I would beg to differ that this map puts Chicago at the edge of a high-tornado zone. It's solidly in one, as is Kansas City.