Musk has zero authority on his own. Rubio, to some degree, has authority. Anything that is being done quite literally has to come from the executive branch otherwise why would anyone listen? If musk came to your house and told you to wash your car, you would tell him to fuck off because he literally has no authority.
Ah! You've got it, by Jove! Well, almost. You're getting there.
1. So you've more or less correctly stated the legal standard: Elon has no authority. It's not quite that simple, because Elon could be given authority to do ministerial tasks. For instance, if Trump said, "we're having a cabinet meeting. I want you to go to Dunkin and get donuts for the meeting. You can charge it to the government," and Elon asks, "what kind of donuts," and Trump says, "your choice" -- that is a ministerial decision. Trump can delegate those types of decisions to anyone. But obviously the ministerial duties are not at issue, so we'll go with "Elon has no authority."
2. The next step is to determine whether Elon has in fact acted consistent with having no authority. To continue your analogy, Elon has no authority to make me wash his car. But what if he shows up with the US Marshals and says, "wash my car," he is wielding an authority he does not have. That's what is illegal. Indeed, most people, faced with the prospect of imminent arrest if they don't follow Elon's orders, would probably wash his car. And that's why Elon has to be enjoined from doing that.
3. So the list of areas where Elon/DOGE appears to have exercised authority that they do not have:
A. The five things email. That's analogous to showing up with the US Marshals for the car wash. Government employees are not in a position to stand up to Elon and say, "no, I will not obey" because that's not their jobs. It's why the government employee union sued. For some reason, the judge said the union didn't have standing -- which appears to be based on a weird quirk of the law, probably because nobody prepared for this situation -- but on the merits, Elon's actions were illegal.
B. Bullying his way into federal buildings. Clearly illegal on your theory.
C. Threatening people with consequences if they don't allow Elon's people to access the computing systems. Again, illegal. Now, if Elon brandishes an order from the president saying, "SSA, you shall give Elon Musk and his team of people access to the systems so that he can gather information to advise me," that illegality would be avoided. Think he has such a document? It also doesn't answer some of the other illegality, like laws that prohibit anyone from accessing tax returns. Or laws committing the operation of agencies to a board that doesn't answer to the president. But anyway, that's all downstream.
D. Directing the firings of all those employees. Here the standard is arguably higher (though again the case law here is underdeveloped), because showing up to Trump with a huge readout of all the employees to hire and getting ratification is not an advisory task. That's like a cabinet member sending a proposed rule making to OMB for ratification. If the cabinet member doing that has not been confirmed by the Senate (or is lawfully acting as an interim head), then it is illegal, unconstitutional and it should be voided.
We good now?
