The Watchtower /Jehovah`s Witnesses believe and teach that the Apostasy began by the time the last Apostle died around 100 AD
To clarify, JW's believe:
1. That apostasy had started even before the apostles died and it increased after 100 AD
2. All books of the new testament were written before 100 AD, or before the great apostasy. No writer was an apostate.
3. St. Clement of Rome, who died in 99 AD, was already quoting from the gospels and the Pauline letters (95 quotes from the 10 of 27 books)
4. Early writers from the first century, Polycarp, Ignatius have quoted from the new testament books, which show that they were already accepted as canonical by Christians in the first century.
Jehovah`s Witnesses accept the word of Apostates who determined what books are to be accepted in the Christian Greek Scriptures NT
In fact, it was the other way round. It was the 'apostates' who questioned the canonicity of certain books of the NT like Hebrews, 2 Peter, James, 2 & 3 John etc throughout the second and the third century whereas these books were already being used by Christians in the first and second century. Questions regarding which books of the Bible should be included in the canon were not fully settled till 16th Century and later (Council of Trent).
Regarding this, a comment was made by NT scholar Lee Martin McDonald: "Although a number of Christians have thought that church councils determined what books were to be included in the biblical canons, a more accurate reflection of the matter is that the councils recognized or acknowledged those books that had already obtained prominence from usage among the various early Christian communities."
As it says, the apostates simply acknowledged the canon which was used by Christians in the first century. In many cases, they questioned some of these authentic books down to the 15th Century.
If JW's accepted the apostates word, then they wouldn't have removed the Apocrypha and the spurious texts from the NT. Neither would they have added the name Jehovah to the NT.