You're wrong, He has the recommendation of the full House Intelligence Committee (his direct oversight) and the chairman of his Senate Intelligence oversight committee both asking for it, which could easily be considered plenty sufficient.
The only people calling for Mueller's appointment were a few ragtag Dems and they got one setup to investigate Trump, so this request for a Clinton SP has significantly more official weight behind it.
“He has the recommendation of the full House Intelligence Committee (his direct oversight) “
You are correct, that upon that recommendation he COULD appoint a SP. But it’s entirely up to him and his boss.
No other party in the world gets a vote on the matter.