A list of such appointees shows this assertion to be an incontrovertible fact. (dailypost.ng)
Rosenstein, who appointed Mueller in mid-May as special counsel overseeing the the investigation into whether the President Donald Trump's campaign colluded with Russian officials during the 2016 election, noted that under the special counsel regulations, only the attorney general has the authority to fire such an appointee. (businessinsider.com)
Most such appointees are members of parties with internally determined leaders. (politics.stackexchange.com)