Note that this article is the Washington Post, owned by Jeff Bezos, a competing oligarch. Oligarch Bezos is also known for setting editorial direction, at least, of WaPo. Is this WaPo article real reporting, or one oligarch sniping at another, or Bezos trying to influence framing of Musk?
Furthermore, "The Washington Post has a content partnership with OpenAI."
That's the bigger deal. It's at a more local level than the ownership, and there's little evidence that Musk and Bezos dislike each other.
At the level of wealth that oligarchs Bezos and Musk are at, I don't believe that there's anything other than direct, no holds barred competition. Each of them is wealthy enough to find a space program after all.