We hold that no one should ever refuse the pope’s authority but that everyone should refuse the pope’s sinful commands. Therefore, we think you are wrong that anyone ever has a “duty to refuse the ordinary authority” of the pope. The opposite is true: we must always accept the pope’s authority, even when we cannot comply with sinful commands issued under color of that authority.
Further, you propose the erroneous novelty that the conciliar apostasy somehow “implies the duty to submit to the authority of extraordinary supplied jurisdiction”. In other words, you assert that the SSPX’s supplied jurisdiction gives the SSPX authority over the faithful to compel their obedience.
This is all nonsense, just like the last open letter to Fr. Themann, and demonstrates the author(s) simply don't have a clue of what they are writing about.
For an Order there is an authority that it must submit to. In the case of the Capuchins the head of the Order (the Minister General) is currently Brother Mauro Jöhri. This is the ordinary authority that Fr. Stehlin is writing about. To not have this submission to authority, this 'link' to the Church, the unity communion, necessarily means the Order would be cut-off from the Church: it would be schismatic.
Realizing that to safeguard the Faith they must refuse submission to the ordinary authority the Capuchins (and the other religious orders) look to another authority - a substitute Minister General, if you will - in the form of the SSPX to maintain this 'link' to the Church and authority; this is the extraordinary supplied jurisdiction that Fr. Stehlin is writing about.
Essentially, the Capuchins have volutarily submitted to the authority of the SSPX where one of it's members will act as Minister General. But this does not give them the right to meddle in the internal affairs of the Society or publicly criticize it's superior general/general council; it is both right and within the power of Bp. Fellay to rebuke both Fr. Jean and Father Guardian.