No, it isn't "private judgment" if one uses the rule of faith to judge. The rule of faith is what the Church taught before.
The 1960s robber council is a robber council because it contradicts Church teaching.
Lookup CI-posts of user drew with keywords proximate rule faith.
But drew believes that the proximate rule of faith is the set of dogmatic doctrines of the Church. This is why he believes Bergoglio is the true pope and also why he believes he can justly resist the pope and use his own private judgment to overrule the pope’s decisions.
The Church on the other hand teaches that obedience to the pope is necessary for salvation. But it was always necessary to use our own private judgment to identify the pope and the true hierarchy of the Church. E.g. St Vincent Ferrar vs St Catherine of Siena during the Great Western Schism.
So if you believe that it is the pope who is the proximate rule of faith, then in order to know what the Church teaches, you first have to identify who is the pope or in the case of an interregnum, who are the legitimate hierarchy of the Church.
In the case of V2, no one disobeyed the supposed pope in 1965. It wasn’t until at least 1967 that anyone questioned the legitimacy of the pope (Shuckhardt). The traditional Catholic movement didn’t start until 1970 at the earliest after the new “Mass” had already been concocted. So it wasn’t a problem with the texts of V2 (although the problems certainly were there) that sparked the traditional Catholic movement, it was the founding of a new religion with the Mass being the most obvious manifestation.
It was only after the fact of the new religion that we traced the problem back to V2. And for sedes, it was traced back to the elections of 1958 and 1963.
If Vigano is going to have any success at uniting the clans he will have to address the new religion and its positively doubtful sacraments. I wonder if he will have the courage to do that since his own legitimacy will come into question.