First of all, there's no need to descend into polemics, and if you approach delicate matters in sacred theology in such a way, you are almost guaranteed to err. I'll be happy to explain and defend the so-called recognize and resist position, and to show you how such eminent Doctors as St. Thomas and St. Robert mention the possibility of authority being abused, even to the point of unjust excommunications issuing from the Supreme Pontiff. But that wasn't the point of your thread here, I'll remind you. And an attack on the non-sede position does nothing to explain the gigantic difficulty this creates for the position that we have had no Pope for 55 years, because there is no one to appoint bishops to office, no one to give them a canonical mission in that scenario, and most bishops who had it have died by now. If you think a bishop cannot belong to the hierarchy just because he is in the Conciliar Church, that is true for all bishops under your idea but not under the Society's.
The Society knows only too well what sedevacantists don't take into account, that the true hierarchy is constituted of those who have received a legitimate canonical mission from the Pope. This doctrine of the faith is why the Society says there are still some in the mainstream or Conciliar Church who haven't totally lost the faith yet and why 55 year sedevacantism is monumentally improbable at best when this is taken into account. Yes, we all know jurisdiction is supplied for certain acts to those who do not have it habitually when there is a state of necessity.
But that is entirely beside the point. Ordinary jurisdiction is necessary for Apostolicity of mission, (and receiving jurisdiction supplied for individual acts is not the same as having ordinary jurisdiction no matter how many times it is supplied) it is the formal component of the same, that power comes from the Supreme Pontiff to the bishops, and while it is possible for the number of the hierarchy that have kept the faith to be greatly diminished (as the Society maintains), the whole Church cannot be deprived of that power, otherwise the Catholic Church has ceased to be Apostolic, which is impossible. Thoughtful sedevacantists should, before they misguidedly berate non-sedes out of their own misunderstanding, ask themselves the question, where is the hierarchy of the Church today, where are the Bishops appointed to offices in the Church by a Pope, having ordinary jurisdiction? They are in the mainstream Church.