It must be understood that when the censure falls upon an individual "automatically," this is only in the "internal forum." An ipso facto excommunication has no effect upon the status of its recipient vis-a-vis the external forum, until the legitimate authorities of the Church establish and certify the incurrence of the censure. Thus, should a bishop preach heresy, he incurs this censure; but he is not thereby expelled from his bishopric, so that his diocese is without a head. That effect of the law occurs only after the juridical requirements of the Code are fulfilled, and the proper authority ratifies the determinations of the proper ecclesiastical tribunal.
Due to a want of understanding of these principles, there are those who have declared that, since the Fathers of the Second Vatican Council incurred the censures imposed by Pope Pius II's Bull, Execra bilis, or those which the Code of Canon Law attaches to public heresy, all those cardinals and bishops lost their offices. Therefore, they insist, the elections of Pope John Paul I and Pope John Paul II by these cardinals were invalid. Since these two Popes were also active at the Council, having been expelled from the Church, they could not have been validly elected. Further still, all the Conciliar Bishops, having been excommunicated for their part in the Council, were automatically deprived of their dioceses. And since Pope John Paul II's election was invalid, not only is the throne of St. Peter vacant, but all his appointments have been invalid also. Therefore, neither the Pope, nor any of the Conciliar Bishops, hold their offices legitimately.
The universal Church is without a head, and all the dioceses throughout the world are without ordinaries. In a layperson, such reasoning would be puerile, but somewhat understandable. Unfortunately, it is promoted by priests. Moreover, acting on such conclusions, certain priests have justified their being consecrated bishops, in order that the Apostolic succession of Orders and jurisdiction not be lost in the Church.
Contrary to such reasoning, it is within the Conciliar Establishment that one finds the historical and structural continuity of the True Church; even though they are serving Satan, those who hold ecclesiastical offices hold them legitimately.
Those who say otherwise have not proved that, because these men are apostates from the Faith, they cannot be considered to hold any offices. "One who is no longer a Catholic," they say, "cannot possibly hold an office within the Church, nor exercise legitimate authority." No, even though these individuals have incurred the censures of the Church's law for heresy, apostasy, the desecration of the churches, the violation of the Sacraments, for these and similar crimes, they continue to be the legitimate authorities of the Church. And since they do hold these offices, others who seek to interpose themselves into authority over the Catholic faithful, commit schismatical acts in doing so, and themselves incur the penalties of the Code.
This passage is key; it backs up what I was saying that Father Wathen was grasping at the distinctions made by sedeprivationism but just failed to explicitly articulate it.
If he would have said, "Once [materially] a Catholic, always [materially] a Catholic." then we're good to go.
Yet "Once [formally] a Catholic, always [formally] a Catholic." then that is false.
So the question becomes, can a purely material Catholic formally exercise jurisdiction in the Church? That's a very difficult question ... something that's very much oversimplified by the vast majority of SVs.
Let's take a look at this example.
Cardinal Cushing is known to have stated publicly, "No salvation outside the Church? Nonsense. Nobody's going to tell me that Christ came to die for any select group."
So Cardinal Cushing was a manifest heretic.
Did he therefore at that very moment cease to be the Bishop of Boston?