I do not really know the extent to which I can answer your question because really it depends on what you would personally consider to be Truth. The least I can hope to accomplish is to inform you about the history that some of these churches have claimed, while I do not know much about the history and origins of the Catholic church or Greek/Russian Orthodoxy. I have spent some time studying the Armenian Apostolic Church as well as the Syriac Orthodox Church, mostly due to the fact that I myself am Armenian and have spent much of my life in close proximity to Syriac Christians.

The history of early Christianity in Armenia and within the Armenia people is rather obscure. The people never really had an alphabet or a writing system for the Armenian language and until it was created by Mesrop Mashtots in the earth 5th century, Armenians used either Pahlavi inscriptions or Greek/Aramaic writing systems. Mashtots went on to then translate scripture and writings of the bible from Aramaic (which is the language that the Syriac Orthodox Church is traditionally liturgized in) into Armenian. It is important to discuss Mesrop Mashtots when talking about the early history of Christianity in Armenia as one of his students, Movses Khorenatsi, went on to become the patmahayr (or the father of the history of Armenians) writing what is considered to be the prominent collection of Armenian history known as the Hayoc Patmutyun (more simply just the History of Armenia).

Prior to Movses Khorenatsi the secretary of King Tiridates III of Armenia (The King converted Armenia and the Armenians to Christianity becoming the first country in the world to adopt Christianity in 301 AD), a man named Agat'angelos also published a collection about the history of Armenia. This is, however, disputed by historians after the 19th century as further research into his writings indicates that he was alive in the 5th century AD meaning that he could not have been alive to be the secretary of Tiridates.

In Armenian tradition, the history of Christianity of Armenia is connected to the apostles Bartholomew and Thaddeus. Legend has it that the Armenian King Abgar of Edessa around 30AD sent a letter to Jesus asking for Jesus to heal him of his leprosy. Thomas the Apostle then sent Thaddeus to Edessa where he healed the King causing the King to convert to Christianity. Abgar sent Thaddeus on a mission to convert other parts of Armenia. This is disputed by some historians with many claiming that the conversion of Abgar is fiction and was made up by early Armenian historians. Tradition then says that after Abgar's death around 45AD Bartholomew had joined Thaddeus and Abgar's kingdom was split between his son Ananun and his nephew Sanatruk. The daughter of Sanaturk was converted by Thaddeus leading to the King ordering the death of Thaddeus and his daughter. Legend has it that the Monastery of Saint Thaddeus was built to commemorate his martyrdom in 68 AD.

Make of these as you will but it is good to remember that these stories come from legends and traditions passed down by generations. The only sources of information that we really have for this, more specifically for the establishment of the Syriac Orthodox Church in Antioch, is the bible and, for the history of Christianity in Armenia, are the writings of historians that lives hundreds of years after these events took place. Attempting to learn the history of this time and especially the history of the beginnings of Christianity at this time is rather difficult as the peoples have been persecuted since the beginning and many had become Christians in secrecy. I do not personally believe it all to be true but generally speaking it is all we have when it comes to this time period, but I do believe there is at least some truth in the legends.