Mr. Musk’s criticism of the agency appears petulant and poorly timed, given his need to have the settlement approved, but it is not the type of statement that misleads shareholders. It does indicate that he may not be as contrite as other defendants who settle with the S.E.C., however, and could violate the injunction. That could have serious consequences by allowing the S.E.C. to ask the federal court to impose additional penalties.

One basis for justifying a permanent injunction is whether the defendant is likely to violate securities laws in the future. The securities laws prohibit both false statements and those that are so sketchy that they could mislead investors — something the 280 characters allowed on Twitter might foster.

The S.E.C.’s settlement with Tesla, which was sued separately from Mr. Musk, requires the company to “employ or designate an experienced securities lawyer whose qualifications are not unacceptable” to the S.E.C.’s staff to review future communications through social media by its senior executives. That person must stay in place as long as Tesla remains a public company, with the S.E.C. apparently hoping that the lawyer will be able to tone down Mr. Musk’s social media commentary. In addition, the company must create a committee of independent directors who will oversee the controls that Tesla has been told to put in place regarding public statements by its executives.

But can Tesla’s board of directors or corporate counsel control Mr. Musk? The S.E.C. will certainly be watching and has the ability to punish him if he makes statements that are considered to be a potential violation.

If that happens, the S.E.C. could pursue a civil contempt case, and Mr. Musk’s tweets criticizing the agency could bolster it.