This seems to be pseudo-history at best, the saying is centuries old in some form or another - Wiktionary has "it never rains, but it pours" at 1772, and even then it was being given as a trite saying.
Maybe it popularised the modern wording, but the story in the article isn't going for that angle at all.
Maybe it popularised the modern wording, but the story in the article isn't going for that angle at all.