Re: Bit klunky, but...
It comes down to respect.
If I call my buddy an asshat in the pub, there are no consequences.
If I drop a Teams message to the CEO, to politely inform him that he made an error in a statement and what the situation really is - this is OK.
Heck, I even thought Musk took the comment in his stride - to be fair he did ask to be corrected?
You never quite know after this point, if Musk fired him, or if his local manager/PR department has realised what a clusterf*** has been created, and they fired him because he had created a mild social media storm (optics are always good within a company, so anyone causing a ruckus on social media must considerable themselves expendable).
Personally, I wouldn't correct my line manager on Linkedin, yet alone a CEO of a billion dollar corporation on his own platform.