The circular logic of the Catholic Church is based on the assertion: "The Catholic Church is always right." It is often covered in several layers of abstraction, but it is always there none the less.
1 Clement starts the whole process and that's the real corner stone of the Papacy.
Catholics will claim it is the keys, but that's further down the circular logic track. First claim primacy, second claim the right to interpret the Bible, then claim primacy through interpretation.
Which came first, 1 Clement or the keys?
It reminds me of the Supreme Court. Some judges look to the Constitution for truth and principle. Other judges look to the Constitution to prove their own belief.
The keys given to Peter are an example of looking to the Bible to prove an existing belief.
Before Christ gave the "keys" to Peter, another momentous event took place.
Mark 3:16; John 1:42 – Jesus renames Simon "Kepha" in Aramaic which literally means "rock." This was an extraordinary thing for Jesus to do, because "rock" was not even a name in Jesus' time. Jesus did this, not to give Simon a strange name, but to identify his new status among the apostles. When God changes a person's name, He changes their status.
Matt. 16:18 - Jesus said in Aramaic, you are "Kepha" and on this "Kepha" I will build my Church.
And there is the Scriptural foundation.
The Catholic church is apostolic. The Bible is not the source of its truths; Christ is, Who is the incarnate Word, and the Church propagates the Word. It is always right because Christ is her bridegroom, not because of a particular verse or a particular encyclical.
Nevertheless, the Scripture, as NYer pointed out, shows ascendancy of Peter at several junctures: the profession of Peter followed by the granting of the new name, promise of Christ's Church built, symbolically, on Peter the Rock, handing of the keys, another profession of Peter's love for Christ, and the charge to feed and guide the sheep. The primacy of the Chair of Peter, nor its location in Rome, was never challenged in the Early Church, as the letter of Pope Clement (among other patristic documents) illustrates. So, the primacy of the Papacy is both scriptural and apostolic.
No, the keys are an ancient symbol of authority and have nothing to do with a Berean like quest for verification of beliefs in Scripture. This is particularly evident since at at the time of the "keying" there was only OT Scripture.