The lie is coming from Musk and his cult of supporters.
You all decided to interpret his gesture as the nazi salute. Big difference.
I allow for the possibility that in the moment he didn't mean for it to be that salute. Now if he's too weak to clarify it wasn't? Then he did a Nazi salute in all ways that count. Being an accidental Nazi is very much on topic for the text we're commenting on.
I mean, he built the world's leading online platform for anti-Semitism with his take on Twitter/X. All the classic anti-Semitic tropes are extremely common, people are being hounded with anti-Semitic slurs, etc. Flags on it are basically ignored. Elon Musk himself has even endorsed some anti-Semitic tweets. Concerns about all of that go back years (this is what sparked the ad boycot a few years back). I have a hard time seeing how anyone denying the pattern here is acting in good faith, especially since there's a significantly overlap with people who analyse critics of Israeli policy wrt. the Palestinians to the subatomic level for possible anti-Semitism.
No reason for him to do that in the first place. It would set a precedent of having to defend himself every time people who dislike him deliberately malinterpret anything he does.