Maybe it popularised the modern wording, but the story in the article isn't going for that angle at all.
It's a shame. Stories like this are fascinating when they turn out to be true. Like how "bucket list" entered the American vernacular so quickly and thoroughly that there are many people who believe the movie was named after a preexisting common phrase.
nowadays though we've got zuckerberg pretending like he invented the term 'metaverse'
You mean like, "kick the bucket"?
My grandmother was the idiom queen (by the time the dementia really took hold, she was communicating in trite phrases just like 'kids these days' communicate in memes) and this was one of her favourites.
The meaning of the saying is fairly straightforward - "pours" being more voluminous than "rains", it's like saying "it never trickles but it floods". Related of course to the London bus, where you wait for ages and then 3 show up at once.
Morton's seems to take the sentiment, but change the meaning - it rains AND it pours, because the "it" changes between those two verbs. A clever play on words to change the meaning of and old idiom - maybe similar to Tesco's "Every Little Helps" that's catchy because it's similar and yet different - but as you say, definitely not the origin of the trite saying about misfortune or luck.
I should have known better. Can’t trust even simple things these days.
https://books.google.com/books?id=V2AEAAAAQAAJ&pg=RA4-PA169&...
"These days," as opposed to that glorious time in the past when you could trust anything some random stranger said to you.
From at least 1726:
https://en.wikisource.org/wiki/The_Works_of_the_Rev._Jonatha...
> "Misfortunes never come alone," is an old and trite saying, and "when it rains it pours" is another phrase like unto it
https://www.google.com/search?q=%22when%20it%20rains%20it%20...
Google's Ngram Viewer seems to trace the phrase to the 1850s, though others have turned up earlier references:
https://books.google.com/ngrams/graph?content=when+it+rains+...
And dialing in more on the period 1800 -- 1950:
https://books.google.com/ngrams/graph?content=when+it+rains+...
Note that OCR and other errors may produce spurious hits or date references, though the record here seems pretty clear.