The problem with that interpreatation is that it doesn't account for Jesus' promise to give Peter the "keys" to the kingdom of heaven as well as the power to "bind and loosen". How exactly can a "statement" be given keys? How can a "statement" be given power? How can a "statement" be given power to loosen and bind?
Have you noticed that Peter is given a special place in the NT? He is the most mentioned Apostle by far. Have you noticed that when the Apostles are mentioned it is generally "Peter and the Apostles"? Peter is the first to speak after Penetecost. He is the first to work a miracle. At the Council of Jerusalem when Peter speaks, the issue is resolved. I could go on and on and on...it is so obvious.
But most importantly, the early christians believed that Peter was given a special office:
Tatian the Syrian
"Simon Cephas answered and said, ‘You are the Messiah, the Son of the living God.’ Jesus answered and said unto him, ‘Blessed are you, Simon, son of Jonah: flesh and blood has not revealed it unto thee, but my Father which is in heaven. And I say unto thee also, that you are Cephas, and on this rock will I build my Church; and the gates of hades shall not prevail against it" (The Diatesseron 23 [A.D. 170]).
Tertullian
"Was anything withheld from the knowledge of Peter, who is called ‘the rock on which the Church would be built’ [Matt. 16:18] with the power of ‘loosing and binding in heaven and on earth’ [Matt. 16:19]?" (Demurrer Against the Heretics 22 [A.D. 200]).
"[T]he Lord said to Peter, ‘On this rock I will build my Church, I have given you the keys of the kingdom of heaven [and] whatever you shall have bound or loosed on earth will be bound or loosed in heaven’ [Matt. 16:18–19]. . . . What kind of man are you, subverting and changing what was the manifest intent of the Lord when he conferred this personally upon Peter? Upon you, he says, I will build my Church; and I will give to you the keys" (Modesty 21:9–10 [A.D. 220]).
The Letter of Clement to James
"Be it known to you, my lord, that Simon [Peter], who, for the sake of the true faith, and the most sure foundation of his doctrine, was set apart to be the foundation of the Church, and for this end was by Jesus himself, with his truthful mouth, named Peter" (Letter of Clement to James 2 [A.D. 221]).
The Clementine Homilies
"[Simon Peter said to Simon Magus in Rome:] ‘For you now stand in direct opposition to me, who am a firm rock, the foundation of the Church’ [Matt. 16:18]" (Clementine Homilies 17:19 [A.D. 221]).
Origen
"Look at [Peter], the great foundation of the Church, that most solid of rocks, upon whom Christ built the Church [Matt. 16:18]. And what does our Lord say to him? ‘Oh you of little faith,’ he says, ‘why do you doubt?’ [Matt. 14:31]" (Homilies on Exodus 5:4 [A.D. 248]).
Cyprian of Carthage
"The Lord says to Peter: ‘I say to you,’ he says, ‘that you are Peter, and upon this rock I will build my Church, and the gates of hell will not overcome it. And to you I will give the keys of the kingdom of heaven . . . ’ [Matt. 16:18–19]. On him [Peter] he builds the Church, and to him he gives the command to feed the sheep [John 21:17], and although he assigns a like power to all the apostles, yet he founded a single chair [cathedra], and he established by his own authority a source and an intrinsic reason for that unity. Indeed, the others were that also which Peter was [i.e., apostles], but a primacy is given to Peter, whereby it is made clear that there is but one Church and one chair. . . . If someone does not hold fast to this unity of Peter, can he imagine that he still holds the faith? If he [should] desert the chair of Peter upon whom the Church was built, can he still be confident that he is in the Church?" (The Unity of the Catholic Church 4; 1st edition [A.D. 251]).
"There is one God and one Christ, and one Church, and one chair founded on Peter by the word of the Lord. It is not possible to set up another altar or for there to be another priesthood besides that one altar and that one priesthood. Whoever has gathered elsewhere is scattering" (Letters 43[40]:5 [A.D. 253]).
"There [John 6:68–69] speaks Peter, upon whom the Church would be built, teaching in the name of the Church and showing that even if a stubborn and proud multitude withdraws because it does not wish to obey, yet the Church does not withdraw from Christ. The people joined to the priest and the flock clinging to their shepherd are the Church. You ought to know, then, that the bishop is in the Church and the Church in the bishop, and if someone is not with the bishop, he is not in the Church. They vainly flatter themselves who creep up, not having peace with the priests of God, believing that they are
secretly [i.e., invisibly] in communion with certain individuals. For the Church, which is one and Catholic, is not split nor divided, but it is indeed united and joined by the cement of priests who adhere one to another" (ibid., 66[69]:8).
Origins of Peter as Pope | Catholic Answers
How can we argue with the church fathers who were closet to the Apostles?