I don't think his personal accomplishments really matter in the face of his support for the far right, crushing hatred of trans people, calling people pedophiles and the absurd amount of misinformation and bigotry that he promotes on xitter.
If SpaceX needs an absolute piece of shit like him in order to succeed, then there shouldn't be a SpaceX.
I've also got a degree in physics and I think it's a valid if kinda wonky use of the word study. They studied whether or not GR allowed this specific thing and that's enough to say it's physically possible. It's not just publishing an idea so much as proving the validity of it within current models, to me a study implies investigation of some kind and that's definitely what went on here.
I've definitely heard it used this way before, even if it is less common. I wouldn't say it's an unwritten rule so much just that people have learnt to infer that there's some direct observation going on.