Often times those who would be loathe to admit "private interpretation"  of Scripture,  nonetheless exercise private interpretion of the Sacred Tradition by setting themselves up as judges of the decisions of the Second Vatican Council, Pope Paul VI and Pope John Paul II. While sometimes this arrogating of judgement extends to doctrinal areas, it typically concerns liturgical matters and even more so the prudential decisions of governance of the affairs of the Church. It is argued that these latter are not covered by infallibility and therefore are subject to the weak decisions of weak men. While an appealing logic at a troubled time in the life of the Church, such an approach is both spiritually and ecclesiastically devisive and very far from the attitude that the First Vatican Council said was the piety of a true Catholic with respect to the Roman Pontiff.

...all the faithful of Christ must believe "that the Apostolic See and the Roman Pontiff hold primacy over the whole world, and that the Pontiff of Rome himself is the successor of the blessed Peter, the chief of the apostles, and is the true vicar of Christ and head of the whole Church and faith, and teacher of all Christians; and that to him was handed down in blessed Peter, by our Lord Jesus Christ, full power to feed, rule, and guide the universal Church, just as is also contained in the records of the ecumenical Councils and in the sacred canons"

... the faithful of whatever rite and dignity, both as separate individuals and all together, are bound by a duty of hierarchical submission and true obedience, not only in things pertaining to faith and morals, but also in those which pertain to the discipline and government of the Church spread over the whole world, so that the Church of Christ, protected not only by the Roman Pontiff, but by the unity of communion as well as of the profession of the same faith is one flock under the one highest shepherd. This is the doctrine of Catholic truth from which no one can deviate and keep his faith and salvation... [Dogmatic Constitution on the Church, Vatican Council I, 1870]