That sounds rather Trinitarian to me. If John and the other apostles rejected the deity of Christ and the concept of God's triune nature, then one has to explain where Polycarp got this idea from -- and how he would come to be appointed bishop of Smyrna by the apostles themselves.
Polycarp also clearly approved of the teachings of his close companion Ignatius of Antioch (A.D. 35 or 50 – 98 to 117). Polycarp writes:
In the above passage, he again affirms the deity of Christ and refers to the Spirit of God, and even mentions that salvation is accomplished by Christ's death upon the cross (which is expressly denied by Surah 4:157-158 in the Qur'an).
In his epistle to the church in Smyrna, he writes,
Again, Ignatius affirms Jesus as "the Divine One", and "Son of God by the Divine will and power", and "the cross of the Lord Jesus Christ". None of those are concepts that are compatible with Islam.
Besides his endorsement by Polycarp, whom we have strong reason to think was approved by apostles, there is also some reason to think Ignatius was probably approved by apostles. For example, in his epistle to the Ephesians, he writes:
This suggests that Ignatius was personally acquainted with the apostle Paul. He also elsewhere mentions Paul and Peter together (e.g. in his epistle to the Romans). Combined with the fact that Ignatius was the bishop of Antioch in the first century, and also that Peter and Paul spent time together in Antioch, this makes it probable that he was personally acquainted with Peter and Paul. Even if he wasn't, however, the fact that he is approved by Polycarp, a disciple of John, is adequate for my case.
“You are initiates of the same mysteries as our saintly and renowned Paul of blessed memory (may I be found to have walked in his footsteps when I come to God!), who has remembered you in Christ Jesus in every one of his letters."
“Have we not all the same God, and the same Christ? Is not the same Spirit of grace shed upon us all?”
"Yes, I ask you also, true companion, help these women, who have labored side by side with me in the gospel together with Clement and the rest of my fellow workers, whose names are in the book of life."Is this the same Clement? The case is not conclusive, but there is some reason to think it may well be. For example, later in the same chapter he writes (verses 21-22):
"Greet every saint in Christ Jesus. The brothers who are with me greet you. All the saints greet you, especially those of Caesar's household."What is interesting about this reference to the members of Caesar's household is that it relates quite well to how Clement closes his epistle to the Corinthians:
"Make haste and send our messengers, Claudius Ephebus, Valerius Vito, and Fortunatus, back to us in peace and joy; so that news of the truce and the unity for which we are praying and longing may reach us the more speedily, and we may the sooner rejoice over your return to order."What's interesting about this is that several cases have been found of the two names Claudius (or Claudia) and Valerius (or Valeria) occurring in combination with reference to servants in the Royal employment. Nero belonged to the Claudian family, and his consort Messalina to the Valerian. I would give it an historical rating of "plausible", albeit non-conclusive, that Paul refers to the same Clement in Philippians 4:3.
Let me conclude by drawing a parallel between what I have argued and the Islamic isnad, i.e. the so-called chain of narration used by Muslims for authenticating their hadith traditions. If Muslims are willing to trust the reported stories about Muhammad over hundreds of years because of “isnad”, then it is inconsistent to reject the chains of transmission that I have written about here, of which we have documentary evidence that is much earlier than exists for the traditions that concern Muhammad.
If Jesus' original disciples were Muslims, then why did they so clearly approve of Paul the Apostle, Clement of Rome, Polycarp of Smyrna, and others? How did the disciples' own students and companions -- whose works are still extant in the case of some -- come to believe doctrines which are so starkly at odds with the Islamic religion?