Sorry, but this story originally came from Bloomberg and I lost all faith in Bloomberg after they refused to retract the SuperMicro story. I will believe it when I see it on the sec.gov website. Until then it's as good as bullshit in my eyes.
He and his legal team will absolutely receive copies of any court filings in this case.
Individual filings won't be on sec.gov. You can check PACER, though.
This filing also indicates Musk's legal team chimed in about the tweet in response to the SEC's inquiry (page five). If that weren't the case, Musk would certainly contest that statement. This bit too:
> "According to counsel, immediately upon seeing Musk's 7:15 tweet for the first time after Musk had published it, Tesla's "Designated Securites Counsel" arranged to meet with Musk, and they drafted Musk's corrective 11:41 tweet together."
For an application to a court seeking that someone be held in contempt of court? Yes, this absolutely would be on sec.gov as a 'litigation release' and there are 2500 such examples listed there. If it were true and the SEC is just waiting to issue a press release, I think it's prudent to actually wait for that rather than believe some apocryphal document.
As for contesting the statement, who knows? He is not exactly the most stable individual these days (which is what makes him and his companies a natural target for shortsellers)