Mueller ought to be [redacted].
That's a joke, son, get it? /Foghorn Leghorn>
That question is essentially a legal one, a matter of law. What is Mueller's subject matter jurisdiction? The original grant is ambiguous, but in principle should track Sessions' recusal. If the subject involves the Trump campaign, Sessions hands it to Rosenstein. Otherwise, Sessions keeps the case.
The Rosenstein memo claims territory that is within Sessions' territory, meaning subject matter that Sessions has not recused from. If Sessions' hasn't recused from it, Rosenstein never had it, and it Rosenstein never had it, Rosenstein couldn't give it to Mueller.
The Rosenstein scope-clarification memo claims territory that never left Sessions' jurisdiction.
Does the memo give Mueller the power/jurisdiction? Well, who has the authority to answer that? If DOJ/Rosenstein/Mueller is the authority, then yes, the memo does the trick.
If DOJ/Sessions is the authority, then no, the memo is evidence that Rosenstein and hence Mueller is out of bounds.
If the court is the authority, the court has to choose between competing interpretations of the circumstances that lead to the appointment of Mueller, and will make findings to suit the outcome that particular judge wants.