The SEC complaint claims that "Musk knew or was reckless in not knowing that each of these statements was false and/or misleading because he did not have an adequate basis in fact for his assertions."

That's good to know -- I think, based on some random article I read a month ago or so, he can beat that charge, because he had concrete knowledge about the Saudi Sovereign Wealth Fund being interested in helping take Tesla private.

Again, I could be wrong, and I really wish I could remember where I found that article...

Musk's tweet said "Funding secured", which has a very different implication than a company simply "being interested".

Right. If he was just complaining and said he was only thinking of taking it private and talking to people he could probably get away with it.

Instead he said he heavily implied that he would take it private and already had all the money he needed from various investors.

There’s a world of difference between those two statements.

He also went on to say a number of things that his board advised were probably impossible, such as bringing all investors along with him if Tesla went private.

In the US, you're not supposed to say anything publicly that can manipulate the stock price. For a person in Elon Musk's position, it is incredibly easy to drum up hype about a stock from a public media source (in this case, Twitter) then secretly sell off stock at the higher price causing it to dip further than it was at before. This is called pump and dumping and is very illegal in the United States (read up on The Great Depression and the stock crash of 1929 for more information).

Any evidence he actually sold stock during the spike, that wasn't already scheduled?

Not that I'm aware of, but stock manipulation is illegal whether or not you actually sell any shares.

He was lying. Very clearly. You probably read some fanboys blog saying he wasn't and rationalizing it away.