The ironic thing is, they try to buttress their claim that Peter was in Rome by claiming he used “Babylon” as a code word for Rome. Which, of course, buttresses the interpretation of some that the “Babylon the Great” of Revelation is also Rome, which isn’t exactly a favorable interpretation for Catholics.
Trapped in their own lies is what that is. And like you said, only reinforces the belief that Rome is the Babylon of Revelation. I couldn't believe the Catholic Church would make the claims about the time Peter spent in Rome when even scripture is clearly refuting them.