"The ironic thing is that those guys were looking for cyclical phenomenon, and so they "detrended" the data: "Regardless of source, the ultra-low frequency variation is removed prior to the analysis". They were looking for cycles of a decade or less, and removed any longer-period variation.

Look at their Figure 1, raw data before "detrending". The caption says "Note the low frequency change in annual abundance over the 111-yr period."--the change they're talking about is positive. If I'm reading this right, they found, but removed, a longterm trend showing an increase in hurricane frequency."

You are incorrect. All you need to do in look at fiqure 1 [after 1945 on graph- quote from article: "Finally, caution is advised in interpreting some of the results presented here, as a bias in the hurricane record
is likely before the middle 1940s"].
Just by looking at graph you tell that trend is not up, if anything it's slightly down- but mostly "appearing" random and fairly flat as far as any long term trend goes. If look at whole graph it *appears* as hurricances increased after '40's- and *appears* like there is a slight peak in 50's [if you are an idiot you might think it due to "post war boom" but it's simply better data collection].