Waltz's main point is probably correct, while his approach thoroughly disreputable. He titles his piece "TurretinFan thinks that Athanasius was mocking Liberius" despite the fact that my actual comment in the aside was merely "it is not unreasonable to think that Athanasius is actually using this passage to mock pope Liberius." The fact that Waltz feels compelled to change my position to a stronger claim regarding Athanasius and Liberius, however, is only the tip of the iceberg.
Rather than beginning his article by addressing Athanasius and Liberius, Waltz immediately attempts to change the argument again to being about whether Athanasius accepted Sola Scriptura, something we've already demonstrated from Athanasius' own writings even on those rare occasions when Waltz has attempted to venture out of the secondary sources (scholars who agree with the conclusion Waltz favors become for the moment "patristic scholars of the highest caliber") into the primary sources (here's an example of interaction over the primary material). You can read more from Athanasius himself here (first example)(second example).
Eventually, Waltz actually gets around to discussing the matter. On the whole, I think Waltz is correct in believing that the editor wished to suggest that the "confession of Peter" might be an allusion to Liberius, rather than suggesting that Liberius was one of Constantine's eunuchs. The reason for thinking this is actually not the reasons that Waltz gives, but from the fact that at this point in the history of Liberius, Liberius had not yet Arianized. That came a few sections later (see Arian History, Part V, Section 41).
In view of this, I've updated my post.
However, Waltz's argument itself is quite unconvincing. He refers the reader to section 36 of the history, which praises Liberius prior to Liberius' lapse. The fact that Athanasius praises Liberius at one point doesn't preclude him from mocking Liberius latter. What might change Athanasius' attitude? the less-than-praiseworthy actions of Liberius.
In fact, Waltz doesn't make reference to the important fact of Liberius' lapse, something that would have seemed helpful to his case, had he been aware of it. The quotation we are addressing is in section 38, after the praise of Liberius in his first state, but before the actual lapse of Liberius in section 41: "But Liberius after he had been in banishment two years gave way, and from fear of threatened death subscribed." (Athanasius, Arian History, Part 5, Section 41)
Why doesn't Waltz mention Liberius' lapse? It's hard to believe that Waltz is unaware of it, after studiously researching the context of the quotation provided. A more likely explanation is that Waltz is invested in a theory that Athanasius never opposed Liberius (see his prior comments here), and consequently Waltz does not want to acknowledge Athanasius' opposition to Liberius. After all, in the present post Waltz states: "This appears to be yet another ill-conceived attempt to portray St. Athanasius as an opponent of Liberius ... ."
What makes Waltz's argument worse is that Waltz actually provides a quotation from Athanasius that proves that Athanasius was not a papist: that Athanasius was not someone who viewed the pope as the universal head of the church:
Now it had been better if from the first Constantius had never become connected with this heresy at all; or being connected with it, if he had not yielded so much to those impious men; or having yielded to them, if he had stood by them only thus far, so that judgment might come upon them all for these atrocities alone. But as it would seem, like madmen, having fixed themselves in the bonds of impiety, they are drawing down upon their own heads a more severe judgment. Thus from the first [FN: In contrast to date of his fall.] they spared not even Liberius, Bishop of Rome, but extended [FN: τὴν μανίαν ἐξέτειναν; vid. ἐκτεῖναι τὴν μανίαν, §42. And so in the letter of the Council of Chalcedon to Pope Leo; which says that Dioscorus, κατ᾽ αὐτοῦ τῆς ἀμπέλου τὴν φυλακὴν παρὰ τοῦ σωτῆρος ἐπιτετραμμένου τὴν μανίαν ἐξέτεινε, λέγομεν δὴ τῆς σῆς ὁσιότητος. Hard. Conc. t. 2. p. 656. [Cf. Prolegg. ch. iv. §4.]] their fury even to those parts; they respected not his bishopric, because it was an Apostolical throne; they felt no reverence for Rome, because she is the Metropolis of Romania [FN: By Romania is meant the Roman Empire, according to Montfaucon after Nannius. vid. Præfat. xxxiv. xxxv. And so Epiph. Hær, lxvi, 1 fin, p. 618, and lxviii. 2 init. p. 728, Nil. Ep. i. 75. vid. Du Cange Gloss. Græc. in voc.]; they remembered not that formerly in their letters they had spoken of her Bishops as Apostolical men.- Athanasius, History of the Arians, Part 5, Section 35
What is the jurisdiction of the Roman bishop according to Athanasius? Is it the whole church? No, it is "Romania," that is to say the Roman empire (not the country we call "Romania" today).
We see this same point again in Section 41 when discussing the lapse of Liberius: "Thus they endeavoured at the first to corrupt the Church of the Romans, wishing to introduce impiety into it as well as others." (Athanasius, Arian History, Part 5, Section 41) Notice that forcing Liberius to sign the Arianizing creed was part of a corruption not of the universal church (according to Athanasius) but of the Roman church - one church to which there were others.
Incidentally, we see the same thing from Theodoret, who describes Leo as "the very sacred and holy bishop of the Church of the Romans, the lord Leo ... ." (Theodoret, Letter 144)
So, while we thank Waltz for bringing some additional light to the matter of Liberius' lapse and Athanasius' opposition to that lapse, we have seen that the more deeply we dig into history the less papist we discover the fathers (in this case, Athanasius and Theodoret) to have been.
UPDATE (updated to correct attribution): While we are at it, we might as well point out Hilary of Poitiers' reaction, described here by
The next weighty piece of evidence which the fourth century has to show is the fall of Pope Liberius in 357, when he not only signed (under severe pressure indeed, and as S. Jerome tells us, Chron. A.D. 357, through weariness of exile) the Arian creed of the third Council of Sirmium, but also anathematized S. Athanasius; an additional incident which destroys the plea sometimes adduced by Ultramontanes in mitigation, that the creed was patient of an orthodox interpretation, and was signed by Liberius in that sense only. It is curious to read the gentle, forgiving, and compassionate language in which S. Athanasius himself speaks of this fall, dwelling in preference on the Pope's earlier confessorship (Ad Solitar.}, and then contrast it with the burning indignation of S. Hilary of Poitiers. After setting down the text of the letter addressed by Liberius to the Eastern prelates and clergy, wherein that Pope says that 'it pleased God to let him know that Athanasius had been justly condemned, and that he had consequently expelled him from communion, and refused to receive his letters,' S. Hilary, on reaching the place where Liberius speaks of the Sirmian creed as Catholic, interjects a note thus—['This is the Arian perfidy. This is my note, not the apostate's. What follows is by Liberius.'] What does follow is the sentence: 'This I have willingly received;' whereon S. Hilary again interjects—['I say Anathema to thee, Liberius, and to thy accomplices.'] And after setting down a few words more of the letter, the Saint breaks out a third time—['Anathema to thee again, and yet a third time, renegade [praevaricator] Liberius'], using similar language yet a fourth time at the close of another letter of Liberius, which he has preserved for us—(S. Hilar. Oper. Hist. Frag, vi.)(as provided in the Church Quarterly Review, Volume 9, pp. 510-11 (1880)
SECOND UPDATE: I see that Waltz has responded again, in similar style to the previous post (link to his response). There's plenty of heat in post, but not much additional light. I think my comments above already adequately address the substance of his complaint. Waltz clarifies his own claims, and the readers are welcome to read his clarifications for themselves.