When someone such as an Assistant US Attorney prosecutes a case, they are derivatively using the prosecutorial power of the US Attorney, or in the case of main justice lawyers, of the AG or other principal officer confirmed by the senate.
OK. Then let's translate it to the Office of the Special Counsel ...
"When someone such as a Special Counsel prosecutes a case, they are derivatively using the prosecutorial power of the U.S. Attorney General or the Deputy AG (both of whom are confirmed by the U.S. Senate) who appointed them."
Your supporting documentation is good but your legal reasoning seems very weak.