He's not. There is one statement I wish Dudley had made to clarify his point, but the statement I wish he had made is implicit in one word he uses.
Let's quickly review the broken window fallacy. Bastiat tells of the boy who breaks a window at a bakery. People in the crowd say that's good. Why? Because then it will give more work to glaziers. Bastiat points out that what's unseen is that then the baker will have less money to buy shoes for his kids. Whereas Bastiat focuses on the fact that the glazier has more work while the shoemaker has less work, I, when I teach this article (and I teach it in every course I teach), focus on the effect on wealth. Net result: same number of windows, but one less (fewer?) pair of shoes. Wealth is destroyed.
Dudley makes two points: (1) an obvious one that libertarians will agree with, and (2) a somewhat less obvious one that libertarians should agree with.
The first point is that the economy will recover. While these wealth losses are awful, the long-run effect is probably fairly small. Or, in his words, "Those effects tend to be pretty transitory,"
His second point is that, in his words, "The long-run effect of these disasters unfortunately is it actually lifts economic activity because you have to rebuild all the things that have been damaged by the storms." That's roughly right. I would have said that that's the medium-run effect but Dudley and I might have the same amount of time in mind and, to a central banker, a year or two is the long run. Bastiat doesn't address this point. Implicit in Bastiat's analysis is a full-employment model in which the number of jobs and the number of work hours is the same but the number of increased hours worked by the glazier is exactly offset by the number of decreased hours worked by the shoemaker. That works fine to make Bastiat's important point. But Dudley is addressing a different point: when people's wealth falls, they will temporarily step up their work effort. The result: real GDP may well by slightly higher than otherwise.
This doesn't mean, as my libertarian friend and some of his commenters said, that Hurricane Irma is good for the economy. Hurricane Irma is bad for the economy. And Dudley agrees that it's bad.
What did Dudley say that should have keyed my libertarian friend into the idea that Dudley thinks Hurricane Irma is bad? One key word: "unfortunately."
Look back at his sentence: "The long-run effect of these disasters unfortunately is it actually lifts economic activity because you have to rebuild all the things that have been damaged by the storms." He wouldn't have used the word "unfortunately" if he had thought Hurricane Irma is good for the economy. When your wealth takes a hit, you work harder to offset the wealth loss, even if you never completely offset it. Your output goes up, but your leisure goes down. You are better off by working harder than by not working harder, but you're worse off than if your wealth hadn't fallen in the first place.
So I wish Dudley had clearly made the distinction between wealth and income (GDP). That distinction was implicit in what he said, but he would have done well to make it explicit.
But claiming that he could have said it better--couldn't we all?--is different from claiming that he said it wrong. He didn't.