Utter nonsense. Irenaeus' imagination notwithstanding, the fact remains that the matter of Roman supremacy was not firmly settled until the papcy of Leo the Great (440-461 AD).
Ignatius wrote to the Roman Church in 110: "Not as Peter and Paul did, do I command you". Dionysius of Corinth in 170 says flat out that Peter and Paul founded the Church of Rome. Irenaeus relates it again in the 160s-170s.
It's entirely unclear that Ignatius was suggesting that Peter had been in Rome preaching. Indeed, the passage you reference begins with "I write to all the Churches, and declare to all men, that I willingly die for the sake of God, if so be that ye hinder me not....", followed by Ignatius' request that the Romans pray for him to have constancy in martyrdom, and then the statement that you cite. However, Ignatius is not saying that Peter and Paul had both been in Rome, commanding them. Rather, he simply and only references the fact of their apostolic authority, contrasting it with his own position as one condemned. Contextually, there's nothing here that suggests what you're saying. At best, it could imply that - as was the case with Ignatius himself - Peter was brought to Rome for martyrdom (though that is also by no means settled on evidentiary grounds). The reference is about authority, not geography. Indeed, from what Ignatius writes, it would seem that Peter and Paul were also commanding the "other churches" that Ignatius alludes to - which again suggests their apostolic authority is in view, likely due to both their positions as "primary apostles" and that they were the two major vessels used by the Holy Spirit to write the New Testament.
As for Dionysius, the problem with the fragments we have left is that they're not a trustworthy source. The last fragment includes a complaint that his own letters were being tampered with by "apostles of the devil" who would add to and take away. This puts us into sort of a logical quandary, since how do we know that anything in them (including, ironically, the complaint itself) is genuine? Nevertheless, shaky evidence which may very well have been adulterated to include fabricated support for the growing move to attribute a primacy to Rome.
As for Irenaeus, well, what can we say about him? True, he does on several occasions mention that Peter and Paul "laid the foundations" of the Roman church, etc. But that's just the problem - it's scripturally impossible. Paul's epistle to the Romans is dated at around 57-58 AD. We know from the chronology of Acts that Paul had not been to Rome prior to this date. When Paul writes to the Romans, he indicates that he had not seen them, but was writing to them out of reputation (similar to what we see with the Colossians church) - Romans 1:10,15. Paul writes to this as-yet unmet group of Christians who were already assembled as a church. Without him. Not started by him, nor even built up yet by him. Further, Catholic tradition says that Peter was pope in Rome between 41-66 AD. Are we to presume that Paul would write an epistle to the church where the First Pope of all Christianity was pastor, and not greet this fellow apostle, or even mention his presence? Ridiculous. Clearly, Irenaeus is wrong on this count. This being so, it seems that Irenaeus is writing what he did more for the purpose of bolstering some claim on Rome's part to special apostolic position - and this could very well apply to Peter as well. Irenaeus is not a trustworthy witness in this regard, and in fact, has his problems throughout. He is, after all, the same guy who thought Jesus died when he was 50, despite the obvious Scriptural impossibility of this assertion.
Gaius mentions the Tropaion of the Apostles at the Vatican in around 200--can that refer to anyone else but Peter? This tropaion, as part of a "red wall complex" under the Vatican, was excavated a few decades ago and the bricks in it dating to the Caesarship of Marcus Aurelius between 147-161.
Of course it can refer to somebody else besides Peter - there were a dozen other apostles besides him, after all. Further, Gaius says that the trophies of the Apostles are at both the Vatican and the Ostian Road. Later tradition associates these with Peter and Paul, but this is a century and a half after the fact. Gaius may be relating a developing tradition (or, likewise, he may have had not the least idea of Peter or Paul specifically in his mind when he wrote this - we'll never know since his works exist only as fragments, which limits our ability to delve context), but as with Irenaeus, the problem with the tradition is that it doesn't accord with Scriptural facts.
As for the "Babylon" connection, let's look at what the Assyrian Church of the East has to say--because unlike Germanic johnny-come-latelies to this issue, these are the folks who are lineal descendants from the original Christians in Babylon. There is actually a belief among them that the Petrine epistle was in fact written from their homeland in Babylon proper. And yet, whaddya know...the Syriac liturgy in multiple places nevertheless asserts that Peter and Paul founded the Church in Rome. If anyone had a reason to refute the Peter-Rome connection, they did. And yet they did no such thing--even after 1500 years of schism with the Church of Rome.
Once again, there are Scriptural deficiencies with this assertion of tradition. Tradition cannot overturn Scripture, so the Syriac traditions and liturgies are wrong. Further, archaeology would seem to agree with Scripture. There's a solid case to be made that Peter's ossuary was discovered in Jerusalem in 1953. Also, what are we to make of the fact that when Venerando Correnti, an Italian anthropologist, examined in 1956 the bones that had been certified by Pius XII as belonging to Peter, he found out that they were really an assortment of bones from a number of individuals, some of them female, and some not even homo sapiens. These were the bones of the "Red Wall", that had been certified as "Peter's Tomb." Clearly, these were not the bones of Peter, despite Pius XII's wishful thinking.
So we take the single most important piece of evidence of Roman primacy from the second century, and we dismiss it with a wave of the hand as Irenaeus's personal "imagination". You have no historical warrant to do that TQC. Particularly since his comments are supported by other events of the second century. The fact that the Corinthians are writing to Clement at all to solve their dispute (no Apostle he). Ignatius' epistles, which are written as a man of authority, until he writes to the Romans where all of a sudden he takes a deferential tone. Victor's response to the Quartodeciman controversy--which shows that he thought (at least) he had the right to excommunicate Churches in Asia for their Easter date.
that's just the problem - it's scripturally impossible..
No. It's not Scripturally impossible. You're making an assumption. There are any number of reasons why Paul doesn't address or mention Peter. Tradition gives Peter a stay in Rome of 25 years, but that's very uncertain, and there's no reason to assume he was in Rome the whole time, particularly as we know that Claudius expelled the Jews probably around 49. Peter may have been in Corinth at one point.
Of course it can refer to somebody else besides Peter.
Like who? Which Apostle was martyred on the Vatican Hill?
Tradition cannot overturn Scripture, so the Syriac traditions and liturgies are wrong.
You simply assume Paul's not mentioning Peter in Romans means the latter *cannot* have founded the Church there. You simply assume Babylon does not mean Rome as it does in all the rest of Christian literature. And then you dismiss every single historical reference as mistaken or invalid because they are "contradicting" Scripture. They are not. Scripture says nowhere *plainly*--Peter was at X place until he died. We have to make inferences, and supplement with historical data.
Clearly, these were not the bones of Peter, despite Pius XII's wishful thinking.
Margherita Guarducci has done some detective work on this. It was not the bones you mention but a set discovered in a loculus that may have been the bones of St. Peter. They are of a 60-ish year old man, and the loculus bears traces of gold and murex fragments as befitting a burial of importance.
In any case, I am not resting this case on the validity of the bones but of the historical record.