Gerry Matatics has an interesting perspective on this. The Church is the mystical body of Christ on earth and it's Magisterium is endowed with the property of its head, and continues (continued) His presence among us. Christ was a king, priest, and prophet, thus a) ruler, b) healer/sanctifier, and c) truth teller.
The Magisterium of the Catholic Church took over all these functions, and has (had) them. So, a) it has (had) real authority, and can (could) bind and loose those under its jurisdiction; it can (could) command, and authoritatively say, "do this; do that" ; b) it has (had) the sacraments to justify and translate men from the state of a fallen progeny of Adam to child of God in a state of grace via the sacraments (whose power is via Christ), and the power to redeem and heal; and, c) it was a truth teller, and relayed all necessary truths of the Kingdom of God.
For something to be the, or part of the, true Catholic Church, it must have all of these powers and attributes.
Matatics notes that no Trad priest or bishop basically has the attributes of a). He cannot tell me I must go to his Mass; He cannot bind me by any command. Unlike a bishop or ordinary in a parish of the true Church where I am, either through himself or through a subordinate priest of his (where the Church was and had the attributes of a)), he cannot exercise any binding authority over me.
Any submission of me to him would be purely voluntary, just as to a Prot minister if I were a Prot.
Thus, the marks of the Church lacking - apostolicity (if you incorporate rule or authority into that mark) - in the chapel of whomever down the street (SSPX, SSPV, CMRI, independent priest or bishop), they cannot be a part of the true Catholic Church.
He is a home aloner, and you can quibble with his response to the state of things. But I think he is clearly right to the extent that we are "free," and how we exercise our Catholic faith in these circuмstances of being "without a representative of the King" to command us will be judged accordingly, and not by standards governing when the King's representative could bindingly say, "do this; do that."
I'm not sure how LT in the original post would shake down on this, because it is a bit confusing. He seems to agree with the above when he says we are "free," but I'm not sure.