Brother, this letter is authentic and official.
I did not state, "whereever Peter is, there is the Catholic Church". I clearly stated, " wherever Jesus Christ is, there is the Catholic Church." - As stated in the letter I provided.
The letter in question, was, "The Epistle of Ignatius to the Smyrnaeans".
The certain part of the letter was, talking about "let nothing be done without the bishops".
http://www.newadvent.org/fathers/0109.htm
If you do not believe the website, it references it's source.
"Translated by Alexander Roberts and James Donaldson. From Ante-Nicene Fathers, Vol. 1. Edited by Alexander Roberts, James Donaldson, and A. Cleveland Coxe. (Buffalo, NY: Christian Literature Publishing Co., 1885.) Revised and edited for New Advent by Kevin Knight"
Feel free to check it brother.
Although, you did state, "Notice Ignatius said nothing about having to follow Peter's successor (in Rome)" - What is true my friend, Ignatius did not say anything about it, but I can reference other early Christians.
Irenaeus:
"The blessed apostles [Peter and Paul], having founded and built up the church [of Rome] . . . handed over the office of the episcopate to Linus" (Against Heresies 3:3:3 [A.D. 189]).
Tertullian:
"[T]his is the way in which the apostolic churches transmit their lists: like the church of the Smyrneans, which records that Polycarp was placed there by John, like the church of the Romans, where Clement was ordained by Peter" (Demurrer Against the Heretics 32:2 [A.D. 200]).
The Little Labyrinth:
"Victor . . . was the thirteenth bishop of Rome from Peter" (The Little Labyrinth [A.D. 211], in Eusebius, Church History 5:28:3).
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. ... ’ [Matt. 16:18]. 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. . . . If someone [today] 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; first edition [A.D. 251]).
"Cornelius was made bishop by the decision of God and of his Christ, by the testimony of almost all the clergy, by the applause of the people then present, by the college of venerable priests and good men, at a time when no one had been made [bishop] before him—when the place of [Pope] Fabian, which is the place of Peter, the dignity of the sacerdotal chair, was vacant. Since it has been occupied both at the will of God and with the ratified consent of all of us, whoever now wishes to become bishop must do so outside. For he cannot have ecclesiastical rank who does not hold to the unity of the Church" (Letters 55:[52]):8 [A.D. 253]).
"With a false bishop appointed for themselves by heretics, they dare even to set sail and carry letters from schismatics and b.asphemers to the chair of Peter and to the principal church [at Rome], in which sacerdotal unity has its source" (ibid., 59:14).
May the blessings of Jesus Christ be upon.