"Let those then who, through the calamities of time, have been cut off, not be slow to pay due respect to this divinely erected and unbroken rock, this Apostolic See for whom to rule is to serve. Let them bear in mind and imitate Flavian, that second John Chrysostom, in his sufferings for justice; and the fathers of Chalcedon, those most worthy members of the Mystical Body of Christ; and Marcian, that strong, gentle and wise ruler; and Pulcheria, that resplendent lily of inviolate royal beauty. From such a return to the unity of the Church we foresee that there would flow a rich fountain of blessings unto the common good of the whole Christian world."
40. Truly we are aware of the accumulation of prejudice that tenaciously prevents the happy fulfillment of the prayer offered by Christ at the last Supper to his Eternal Father for the followers of the Gospel: 'That they may be one' John xvii, 21).
We desire then and we wish that all those who have at heart an earnest invitation to Christian unity —and surely no one who belongs to Christ would belittle the importance of this matter—should pour forth their united prayers and supplications to God, from whom comes all unity, order and beauty, that the praiseworthy desires of every right-thinking person may soon be brought to fulfillment. Let research be made without jealousy or anger to straighten out the path by which this good may be reached; let us bear in mind that today we are accustomed to retrace and weigh the events of bygone ages more calmly than in the past.
And Pius XII goes on and on about the need for all of the separated to return. It's the Catholic ecumenism of return. The only ecumenism that is viable. JPII is not willing to go this far in UUS. He dances, skirts and wastes a lot of peoples time and energy with his indirection and misdirection.
"To believe in Christ means to desire unity; to desire unity means to desire the Church; ... The elements of this already-given Church exist, found in their fullness in the Catholic Church" (UUS 9, 14). Looks like "ecumenism of return" to me.
It would seem that you are simply unable to read JP II's plain words:
9. Jesus himself, at the hour of his Passion, prayed "that they may all be one" (Jn 17:21). This unity, which the Lord has bestowed on his Church and in which he wishes to embrace all people, is not something added on, but stands at the very heart of Christ's mission.
That is exactly what Leo XIII, Pius XI, and Pius XII, said.
Now here is the "false opinion":
For authors who favor this view are accustomed, times almost without number, to bring forward these words of Christ: "That they all may be one.... And there shall be one fold and one shepherd,"[14] with this signification however: that Christ Jesus merely expressed a desire and prayer, which still lacks its fulfillment. For they are of the opinion that the unity of faith and government, which is a note of the one true Church of Christ, has hardly up to the present time existed, and does not to-day exist.
It is that "the unity of faith and government ... does not to-day exist", and that this may be deduced from "Ut unum sint". Compare to JP II's teaching in UUS, which is the exact opposite of the false opinion:
11. The Catholic Church thus affirms that during the two thousand years of her history she has been preserved in unity, with all the means with which God wishes to endow his Church, and this despite the often grave crises which have shaken her, the infidelity of some of her ministers, and the faults into which her members daily fall.