I had time to read through the tract on catholic.com that you linked to. It's a pretty good read. They bring up the same point I did - "On the other hand, if Peter never made it to the capital, he still could have been the first pope, since one of his successors could have been the first holder of that office to settle in Rome."

A little later, it says "No, somehow the question [of Peter ever being in Rome or not], while interesting historically, doesn’t seem to be crucial to the real issue, whether the papacy was founded by Christ."

It looks like the Catholic church, while indeed claiming that Peter did go to Rome, does not require that for him to still be the first pope and therefore the first bishop of Rome.

That's why I was wanting the OP to clarify - to make sure he or she was just asking about Peter having been to Rome or not.

Another possibility the OP could have in mind is that Peter did go to Rome, but was never the bishop there.