He has the right to say the Tridentine Mass. If his bishop denies him this right, the bishop is the disobedient one, not the priest, since Quo Primum has never been abrogated. Fr. Z is on very firm legal ground.
Pope ultima has spoken. Even Michael Davies admits that Quo Primum was (likely) obrogated by Missale Romanum. Any right to say the 1962 Missal today would come from immemorial custom.
We have no official prohibition and I think that the Pope would never establish an official prohibition not because of the words of Pius V, who said this was a Mass forever. Those words of Pius V were common for an important decision of the Pope. He always said, "This is valid forever." But this was not a theological, it was not a dogmatic statement, this decree of the Pope promulgting his Tridentine Mass order. And so it could be changed by his successors....In Italian, they say that one pope gives the bull and another takes the bull again, that is, he can change the disposition of his predecessor...
So what about a bishop forbidding the Mass in the case of a priest or a whole dioceses? You must realize that a bishop is the only one who has responsibility for his dioceses....Bishops have no jurisdiction over their collegues. A bishop in his dioceses, for his dioceses and his subjects, can find the arguments to forbid it. He can say, "This is disturbing to the peace in the dioceses."
It is necessary to notice that the privilege is given to the bishops, not the faithful. So a bishop can use the privilege or not. (Alfons Cardinal Stickler, Interview in Latin Mass Magazine Summer 1995)