Rashi says that one of the meanings of Aharon's prayer regarding Miriam ("Let her not be like the dead, which comes out of his mother's womb with half his flesh consumed!"; Bamidbar 12:12) was that there is no way for her to be purified from her Tzara'as except through a miracle.
Another interpretation: Let her not be like the dead-If You do not heal her through prayer, who will confine her? Who will cleanse her? I myself may not examine her, since I am related, and a relative many not examine plague marks [symptomatic of tzara’ath], and there is no other kohen in the world. This is the meaning of, “since he has come out of his mother’s womb.” [Sifrei Beha’alothecha 1:42:12, Tanchuma Tzav 13]
However, while Aharon cannot pronounce her pure, he would presumably unable to pronounce her impure (for the same reason - she's a relative). The law by a Metzora is that if a Kohen doesn't pronounce one a Metzora, he is Tahor.
So the same way Aharon (presumably) made her Tamei, he should make her Tahor?