Usually when I hear this statement, a few clarifying questions show that the person making the claim is just passing on information they’ve heard and have never really investigated it for themselves. Fortunately, I have studied and researched it and I’ll go ahead and set the record straight.
Let’s start with the Old Testament (OT). The most common argument I’ve heard is that books were added to the Old Testament until 100AD with some books being debated until 200 AD. I'm sorry but this just isn't true. The Talmud (teachings) was being compiled during this time, but those are different than the original Hebrew texts. Although Scholars disagree on an exact date, we can say for certain that the Hebrew Bible was completed by around 250 B.C.. This was the time the Septuagint was created FROM the Hebrew Bible TO a Greek translation. (The Septuagint is the Hebrew Bible [Old Testament] written in Greek for Jews living outside of Israel that didn’t speak Hebrew anymore). By necessity a Hebrew Bible had to be present to have a translation made. The Septuagint was very familiar by people of Jesus' day and quoted by many New Testament (NT) authors.
The Dead Sea Scrolls have provided an amazing insight into the age of the OT manuscripts. Vast manuscripts were found including every single book of the Old Testament (except for Esther). These scrolls when compared with the Masoritic texts (dated at 900 AD) show them to be virtually identical. The Dead Sea texts are dated at 125 BC so we can say for certainty that even if we disregarded all the other evidence we have, Isaiah was in its complete form by 125 BC at the ABSOLUTE LATEST. As if this weren't compelling enough, Josephus, a Jewish Historian (who was not a Christian) wrote of the closing of the canon (by name, identical to our current books) as occurring in 4th century BC. It seems ridiculous for us 2000 years later to disregard a secular Scholar living during the time in question.
Now let’s look at the New Testament. First, the complete canonization (canonization means declaring the books of the Bible to be the Holy Word of God) of the Bible (both OT and NT) occurred in 393 AD at the Synod of Hippo. Up until this point, people had little problem determining authentic Scriptures (the Word of God). However, soon various counterfeit "Scriptures" were going around and combined with the edict of Diocletian (303 AD) which required destruction of Christian sacred books, it became apparently clear we needed an "official canon." It should be important to note that the church "determined" the canon much the same way a jury will "determine" a verdict, or a student "determines" an answer, but the church did not have any authority over the canonical works. That is, a book didn't become Holy just because the church said it was. The church used the following criteria to establish the extent of the NT canon:
1. Was the authorship by an apostle or close friend of an apostle?
2. Was the author a Christian leader from the church's first generation?
3. Is it supported by historical traditions as to the writings' authorship and authority?
4. Was it accepted and used by churches throughout the known world?
5. Is it in consonance (complete agreement) with known NT writings and the church's "rule of faith"?
It should be noted that only criteria # 1 was, by itself, sufficient to merit inclusion in the canon. These criteria were combined with the teachings of the apostles to "test the Scriptures." Also, remember that during this time people were being executed over their faith, therefore they didn't just haphazardly decide to include some books but not others. They knew full well they could be killed over these books so they had extra incentive to make sure they were legitimate. Finally, we know that between 13 and 22 of the NT books (that is all but 5 of them) are for sure Scripture based off of other statements in the Bible. (i.e. 1 Tim 5:18, 2 Pet. 3:16, etc.).
Hopefully now you have a little bit more understanding as to how our Bible came to be. As we have seen, the canonization was just a process to make the Scriptures that were already being widely used, including by Jesus Himself, as the complete and true word of God. I believe that it is now apparent that contrary to popular belief, in the case of the Bible there is no correlation between date of canonization and the truthfulness of the words.