A fellow going by the on-line name "Jordanes" made an excellent observation here, namely, that the language of Summorum Pontificum fundamentally answers a juridical question and not primarily a liturgical one. It establishes the legal basis on which a priest of the Roman Rite can say either rite without "permission":
The word "rite" has different shades of meaning. Juridically, the 1962 Missal and the 1970/2003 Missal are two uses of the one Roman Rite -- but in the sense that the differences between the uses are much, much more numerous than the similarities, one can distinguish them as two different rites.
The decree that they are two uses, not two separate juridical rites, is supremely important, because if they were two different rites in the eyes of the liturgical law, then priests in the Latin Rite would need an indult to celebrate according to the 1962 Missal. However, since the Pope has made clear that they are two uses within one rite, all Latin Rite priests have permission to celebrate according to either the 1962 Missal or the 1970/2003 Missal, without having to obtain an indult from their bishop. In other words, if a Latin Rite priest wants to celebrate a "Tridentine" Mass, he may do so -- he doesn't have to ask his bishop first, and he doesn't even have to wait for a group of lay Catholics to approach him and ask him. He has that legal right as a Latin Rite priest with faculties to celebrate Mass according to his own rite, the Roman Rite. (This is better than the "universal indult" that traditionalists had desired -- the Pope says Latin priests don't even need an indult, whether universal or not.)
All the same, the debate about whether or not the two juridical uses are de facto different rites remains open.
Another fellow in that same combox characterized my argument thus:
In order to maintain the opinion, he argues that various practices (read: abuses) in how the Pauline Mass is observed amount to it being a different rite (at least in those instances). Pope says no. Palm says yes. I go with the pope, because he is the head of the Catholic Church.
In a soon-coming post I will have a few words to say about my participation in that discussion (the short take is that I shouldn't have been there or done that). I think most readers will see that I did not directly contradict the Pope, as charged. And it is only fair to point out that I did not argue in my posting below that the Pauline rite is a separate rite based on abuses of it--everything I cited as examples are approved by the Vatican.
Ultimately my position is derived from the much more complete presentation and much greater expertise of Msgr. Klaus Gamber in his very important book The Reform of the Roman Liturgy: Its Problems and Background (bottom line is, if you're going to engage the traditionalist position on the liturgical reform, you have to read this book: period.) Msgr. Gamber goes well beyond the common sense approach of "Hippler's Law" (Arthur would kill me for calling it that), that Different Words + Different Rubrics = Different (Liturgical) Rite. Msgr. Gamber provides a detailed definition of what a liturgical rite is and why the Gregorian rite (or, as he calls it, the ritus romanus) must be considered a different liturgical rite from the Pauline rite (ritus modernus; and for Gamber this would be true even when the Pauline rite is celebrated entirely in Latin using the more traditional options.) I strongly urge a thoughtful reading of this book by an author whom none other than Cardinal Joseph Ratzinger called, "the one scholar who, among the army of pseudo-liturgists, truly represents the liturgical thinking of the center of the Church."
Which brings us again to Cardinal Ratzinger, now Pope Benedict. Quite contrary to this position being flatly contrary to Summorum Pontificum, I really do think that the 1998 talk to Una Voce provides a hermeneutical key to the document. At the very least it helps us understand how and why Cardinal Hoyos, whom the Holy Father himself put in charge of the implementation of Summorum Pontificum, would continue to use language that suggests that the traditional Roman liturgy really is a separate liturgical rite from the Novos Ordo. If someone really has a problem with speaking of the TLM and NOM as distinct liturgical rites then by all means take it up with Cardinal Hoyos. I just agree with him.