So thanks for doing the digging. I upvoted you, and everyone else who linked to earlier usages.
If Morton Salt is trying to take credit for coming up with the saying, shame on them, but somehow I doubt they are. So doubly shame on historydaily.org for pushing a false narrative.
It goes to show that you can't blindly trust whatever you read, even on a .org site.
A domain ending in .org tells you that the owner chose a .org. Nothing else.
Of course, even then slashdot.org existed so the distinction wasn't really effective; later it DID become a bit of a signal because the "big three" were more expensive than .biz and friends so the latter became known for scam/spam sites.
Now it's all completely random and doesn't matter at all.
It has never been the case that you needed to be any particular kind of organisation (or an organisation at all) to get a .org, but in the early days it did tend to be used more by non-profits and the like.