Let's see.
“In 1075 Pope Gregory VII in his Dictatus Papae (The Pope's Memorandum) put it more bluntly. He set out 27 propositions about the powers of the office of Bishop of Rome. These included the statement that the papacy “never will err to all eternity according to the testimony of Holy Scripture”.
(1) Gregory VII never wrote a work entitled "Dictatus Papae". Its title itself suggests its true origin: that it was written by some papal secretary.
(2) No source even mentions the existence of this document until 1087, two years after Gregory VII's death. His actual letters that he personally wrote in 1075 were well-known and a matter of public record during his lifetime. Not only did Gregory VII definitely not write it himself, there is no evidence he was even aware of the document's existence.
(3) The actual text reads: "That the Roman church has never erred; nor will it err to all eternity, the Scripture bearing witness."
This is precisely the Catholic doctrine that the Church is prevented from any error in its dogmatioc teaching, as guaranteed by Matthew 16:18.
So your source does not give the full quote - it substitutes "papacy" for the "Roman Church" of the original. Moreover it insinuates that "the papacy" means individual Popes.
The Church is the institution. The Papacy is an office within that institution. And the individual Popes are all just officeholders.
Conflating the three doesn't work.
STEPHEN VII (896-897AD) "He dug up a Corsican predecessor, Pope Formosus (891-896), when he had been dead for over nine months….
First, the Pope accused of this was Stephen VI, not Stephen VII.
Second, Formosus was not a Corsican, but a Roman.
Third Formosus had been dead for months, but no one knows exactly how long or exactly when this "corpse trial" was held.
Why even lie about these details in the first place? Why fabricate stuff that is unnecessary to fabricate.
And, of course, the "corpse trial" was not held at the request of, or organized by, the elderly and infirm Pope Stephen VI but by Guido IV - the would-be dictator of Rome who hated Formosus for opposing his attempts to seize Italy.
Guido IV was a maniac who did all kinds of disturbed things like this. He was assassinated by rivals a few months after this.
The "corpse trial" was the work of an angry civil dictator, not the Pope.
Misrepresentations folded in completely gratuitous lies.
From The Catholic Encyclopedia concerning Dictatus Papae:
” Sackur (see below) has made it probable that the so-called “Dictatus Papæ” (see GREGORY VII) were composed by Deusdedit. These are twenty-seven short theses concerning the privileges of the Roman Church and the pope [ed. Jaffé, Bibl. Rer. Germ., (Berlin, 1864-) II, 174]. Until quite recently Gregory VII himself was generally regarded as the author; Löwenfeld (see below) continued to maintain the authorship of Gregory, but Sackur, however, has shown that the “Indices capitulorum” in the “Collectio canonum” of Deusdedit are closely related to the brief theses known as “Dictatus Papæ” both in respect of sense and verbal text. Most probably, therefore, the latter are taken from the collection of Deusdedit, who put them together from the “Registrum Epistolarum” or letterbook of Gregory. Possibly also Deusdedit was the editor of this famous and important collection of Gregory’s correspondence. In this case, the cardinal appears in a new light as intimate counsellor and intellectual heir”
So as authorship nothing positive but possibly compiled from Gregory’s letters which would explain its being known after his death.
The quote containing “papacy” was from a BBC writer, Peter Stafford. He should have said Roman Church but then again the teaching is Papal Infallibilty as well as church infallibility. Says The Catholic Encyclopedia under “Papal Infallibility”: “the infallibility claimed for the pope is the same in its nature, scope, and extent as that which the Church as a whole possesses; his ex cathedra teaching does not have to be ratified by the Church’s in order to be infallible.”
It says “pope”, the individual not the office, so who’s conflating?
So you really can’t say Gregory didn’t or did write this Dictatus Papae and you certainly can’t say a secretary wrote it.
So where are the “lies”?