Here, Pope Francis speaks for his predecessor. Is there anything unfairly presented here?
In making their decision they were confident that such a provision would not place in doubt one of the key measures of Vatican Council II or minimize in this way its authority: the Motu proprio recognized that, in its own right, “the Missal promulgated by Paul VI is the ordinary expression of the lex orandi of the Catholic Church of the Latin rite”. [Summorum Pontificum]
This looks right to me: neither John Paul II nor Benedict XVI envisioned anything other than the 1970 Missal being, as quoted here, the “ordinary expression.”
The recognition of the Missal promulgated by St. Pius V “as an extraordinary expression of the same lex orandi” did not in any way underrate the liturgical reform, but was decreed with the desire to acknowledge the “insistent prayers of these faithful,” allowing them “to celebrate the Sacrifice of the Mass according to the editio typica of the Roman Missal promulgated by Blessed John XXIII in 1962 and never abrogated, as the extraordinary form of the Liturgy of the Church”. [Summorum Pontificum]
This one is mixed. Some lay people insisted? Check. The hope it would not denigrate reform? Well … Never abrogated? Well, it was replaced, with the expectation of full replacement by a reform. The gradual nature of this superceding was quick by church standards: 1965, 1967, 1970, and 1975. And first, concessions were made for older clergy, then an expansion with its own agenda in the 1980s.
According to Pope Francis, his predecessor clearly thought that Vatican II acceptance was otherwise or mostly maintained by those celebrating according to the 1962 Missal:
It comforted Benedict XVI in his discernment that many desired “to find the form of the sacred Liturgy dear to them,” “clearly accepted the binding character of Vatican Council II and were faithful to the Pope and to the Bishops”. 
No problem either with the two forms prayed in the same parish:
What is more, he declared to be unfounded the fear of division in parish communities, because “the two forms of the use of the Roman Rite would enrich one another”. 
Was mutual enrichment a real thought? The 1962 Missal provides for far fewer options and far less improvisation. Readings in the vernacular, or other 1965-67 developments? I’m not aware of any such thing being allowed.
Pope Benedict knew he had skeptics across the episcopacy, yet he put his own credibility on the line:
Thus, he invited the Bishops to set aside their doubts and fears, and to welcome the norms, “attentive that everything would proceed in peace and serenity,” with the promise that “it would be possible to find resolutions” in the event that “serious difficulties came to light” in the implementation of the norms “once the Motu proprio came into effect”. 
Pope Benedict did make provision for a reexamination in the case of significant problems. Whether or not the situation in 2021 has found us in “difficulty” is a matter of prudential judgment. Now we know where Pope Francis stands. And we’ve heard like concerns from bishops.
 Benedict XVI, Letter to the Bishops on the occasion of the publication of the Apostolic Letter “Motu proprio data” Summorum Pontificum on the use of the Roman Liturgy prior to the reform of 1970, 7 july 2007: AAS 99 (2007) 796.
 Benedict XVI, Letter to the Bishops on the occasion of the publication of the Apostolic Letter “Motu proprio data” Summorum Pontificum on the use of the Roman Liturgy prior to the reform of 1970, 7 july 2007: AAS 99 (2007) 797.
 Benedict XVI, Letter to the Bishops on the occasion of the publication of the Apostolic Letter “Motu proprio data” Summorum Pontificum on the use of the Roman Liturgy prior to the reform of 1970, 7 july 2007: AAS 99 (2007) 798.
Here are the important links: