Yes, that is right, and anyone could bring the case. I doubt it will be a party in the action.
Equal separation of power would be another.
The courts have granted the executive branch special powers in matters of life and death however.(for example, the power of parole)
It will be interesting and a new precedent if it happens in this case.
I think that just about says it all regarding which branch is currently above itself, don't you? The public (through the Constitution) "grants powers." The courts have no authority.