Yes, typically, the mention of St. Andrew the First Called Apostle's "founding" of the Church of Byzantium (later renamed New Rome and became known as Constantinople) is prefaced with "tradition holds that." Not to diminish Fr. Thomas' vast knowledge of the Church and his exceptional witness and contributions to the Church, I am of the opinion that these exceptionally well educated and well read theologians, typically are victims of Western Christian scholarship which I'm sure asserts that there is no documentation of St. Andrew's founding of the Church of Byzantium. As noted above, however, the synaxarion does tell us that "he left the Apostle Stachy's as the Church's first bishop."
On another note as to an issue raised above, there were many churches founded by Apostles, which are discussed in the New Testament, Ephesos, Thessalonica, Corinth, etc; however, the sees that were honored by the early Ecumenical Synods (Councils to use Western terminology), recognized as "patriarchates," were centers of the church due to their civil prominence in the Roman Empire, except for Jerusalem, which was honored due to its having been the area of the earthly ministry of Jesus Christ. Alexandria and Antioch were provincial capitals. Rome of course, discounts this opinion because it wants to believe it was the center of the church, or the first throne of honor, because it was founded by St. Peter the Apostle, the Chief Apostle, (Orthodoxy also grants the title "Chief Apostle," to St. Paul), but it was honored by the Church because it was the capital of the Empire. When Constantinople was recognized as second in honor to the Church of Rome, it was stated "because it is New Rome." The Church's recognition of the Church of Cyprus' autocephaly, corroborates this logic of the honor the Church bestowed upon what would become known as the Pentarchy, as it has Apostolic foundation by St. Barnabas, but was not recognized as a patriarchate.