Legally, Musk has to pay Tesla for this, and someone very senior at Tesla (the board or the senior executive team) has to approve – without Musk being in the room. But, why wouldn't they say "yes"?
So I don't think this story is fundamentally implausible. (As I pointed out in a comment on another post, the "code review" was probably actually an "architecture review", but it is easy for non-technical people to elide the difference.)
that's not true at all. there's no law that says Twitter/Musk has to pay Tesla engineers anything. it's only up to Tesla's management to decide what they want in return for those resources. Also, as CEO there's nothing stopping Elon from using all of Tesla's resources to help Twitter or any other company. it is entirely up to Tesla's board and shareholders to punish Elon for what should be a gross misappropriation of Tesla's resources
As well as the corporate law issues, the accounting and taxation implications of non-commercial transactions with other firms with which you have significant common ownership can be quite messy in many jurisdictions, which is another compelling argument for keeping those transactions on a commercial fee-for-service basis.
there isn't even a need to see a lawyer about this. there's literally no issue here for the company to ever get sued over. the only risk here is for Elon himself to be reprimanded by the Tesla board. and the chances of that happening are below zero.
All major companies employ in-house lawyers. Issues like this always go through in-house legal. Rather than a question of whether they “need to see a lawyer”, their own lawyers will be advising them on it as a matter of course.