Is there context beyond the "There is a tiny possibility there might be more to this story than meets the eye" tweet he posted? I think if that's the only context reasonably you can interpret that a number of ways: it responding to a dubious claim with a dubious claim is not the only way.
At the level of Elon Musk's influence, if something you can say is so uncertain that there is an uncharitable interpretation you can drive a truck through, I think that arguing that he meant it the charitable way is kind of meaningless when it's just as easy for people to interpret it as his support for the conspiracy theory.
We don't live in Elon Musk's head and someone, at a personal level, can choose to take it as the GP's interpretation, but I think "Context is important" doesn't make sense at all when we all have the same context with different possible interpretations.
You're preaching to the choir. I wish he'd think a bit more before tweeting, because I know what he says can have consequences.
However, that doesn't mean I have to interpret his tweets in the worst possible way, or that I can't remind other people of basic principles of civility.