This is what We exceedingly long for and in suppliant prayer earnestly beg of the Giver of celestial gifts, namely, that the ardent desire of all good men be at last fulfilled, that all may be one[41] and all return to the unity of the fold, to be fed by a single Shepherd.[42] (Pius XII, Ecclesiae Fastos §37)
Is that the "false opinion"?
Unless you can tell me exactly what JPII means when he says He's "open to a new situation." regarding the Petrine Primacy, you are going to have to admit that it goes head to head against Vatican I.
JP II explicitly says that universal jurisdiction and infallibility are essential and can't be changed, and that all that could be changed is practice. How does that go head-to-head with Vatican I?
With the power and the authority without which such an office would be illusory, the Bishop of Rome must ensure the communion of all the Churches. For this reason, he is the first servant of unity. This primacy is exercised on various levels, including vigilance over the handing down of the Word, the celebration of the Liturgy and the Sacraments, the Church's mission, discipline and the Christian life. It is the responsibility of the Successor of Peter to recall the requirements of the common good of the Church, should anyone be tempted to overlook it in the pursuit of personal interests. He has the duty to admonish, to caution and to declare at times that this or that opinion being circulated is irreconcilable with the unity of faith. When circumstances require it, he speaks in the name of all the Pastors in communion with him. He can also—under very specific conditions clearly laid down by the First Vatican Council— declare ex cathedra that a certain doctrine belongs to the deposit of faith.152 By thus bearing witness to the truth, he serves unity.All this however must always be done in communion. When the Catholic Church affirms that the office of the Bishop of Rome corresponds to the will of Christ, she does not separate this office from the mission entrusted to the whole body of Bishops, who are also "vicars and ambassadors of Christ".153 The Bishop of Rome is a member of the "College", and the Bishops are his brothers in the ministry.
Whatever relates to the unity of all Christian communities clearly forms part of the concerns of the primacy. As Bishop of Rome I am fully aware, as I have reaffirmed in the present Encyclical Letter, that Christ ardently desires the full and visible communion of all those Communities in which, by virtue of God's faithfulness, his Spirit dwells. I am convinced that I have a particular responsibility in this regard, above all in acknowledging the ecumenical aspirations of the majority of the Christian Communities and in heeding the request made of me to find a way of exercising the primacy which, while in no way renouncing what is essential to its mission, is nonetheless open to a new situation. For a whole millennium Christians were united in "a brotherly fraternal communion of faith and sacramental life ... If disagreements in belief and discipline arose among them, the Roman See acted by common consent as moderator".154 (Ut Unum Sint §94-95)
What specifically is the "new situation" he is referring to?
No.