Not quite. You can't intentionally say things for the purpose of manipulating the price, you can still say things if they affect the price -- it is impossible not to, since every little thing a CEO does affects the price to some extent (econophysics?).
The lawsuit would have to prove that Musk tweeted with the intention of manipulating the price. Seeing as Musk has always been wary of being public, it seems unlikely he engineered the tweet to do this. Occam's Razor would suggest that he's getting sick and tired of being public (ironically, for this exact reason) and tweeted that he would rather just take it private to avoid this sort of drama.
This is a clear statement of facts, something that would be entirely reasonable to trade based on. It also appears he knew this was a false statement, at best it was very reckless. I really don't see how you can defend this.
When your words make people gain or lose 9 or 10 digits of money in a matter of hours, they are taken very seriously.
Uhhh you mean like the endless rants about trying to get rid of short sellers? That isn't enough to establish a motive for you?