Isn't the author exaggerating in the other direction? There is obviously correlation between the two time series. Sure, who's saying there is causation (as mentioned in the article there can be a third random variable that the first two depended on)? But also, who's to say there's no causation? Is it ok to always remove the correlated part of the two time series? What if that's the interesting part and the explanation you're looking for?
Even if you're looking for causation, detrending is usually necessary to obtain consistent estimators (in statistical terms). For example, Granger causality works with two stationary timeseries:
