This question actually centers on the KJV translation itself. It's not hard to find a church in America (particularly in the south) where they believe that the KJV is the one true translation and that all others are inferior. Why is it the KJV in particular that has achieved this status? Is it because it was the primary translation used for centuries?
The King James (KJV) was translated from a different Greek text than most modern translations. In the early 1500s, Desiderius Erasmus took the best copies of the Greek New Testament available to him, and compared and collated them to create the Textus Receptus (TR), the first Greek New Testament to be printed rather than hand-written.
The TR was the Greek text used by the translators of the KJV as well as other early translators such as William Tyndale and Martin Luther.
In more recent years, thousands of ancient Greek manuscripts—including fragmentary copies as old as the 2nd century and whole New Testaments as old as the 4th—have been rediscovered. Many of the oldest manuscripts consistently disagree with the TR in many places.
For example, the Lord's Prayer in Luke 11:2 begins simply with "Father" in the oldest manuscripts, but "Our Father in heaven" (matching the wording of Matthew 6:9) in the TR.
Most modern scholars agree that it is more likely that Luke 11:2 originally said "Father", and that later copyists substituted Matthew's more expanded phrase—either out of reverence or because Matthew's language is more memorable. It makes more sense that the language of the two passages would converge over time than that it would diverge.
There are many other similar examples. 1 Corinthians 9:1 says "Jesus" in the oldest manuscripts, but "Jesus Christ" in the TR. 2 Corinthians 5:18 says "Christ" in the oldest manuscripts, but "Jesus Christ" in the TR. Again, it's easier to understand how the language would converge on a standard phrase over time.
Furthermore, the age of the manuscripts is evidence of their being closer to the original.
But KJV-only proponents have a different view. To them, the fact that these manuscripts were lost in the first place is reason enough to reject them. KJV-only proponents argue that the manuscripts the TR was based on were preserved because they were the most faithful to the original. According to this view, there are no early manuscripts from this tradition because they were used until they wore out; the other, inferior manuscripts were discarded and have only survived by accident.
Proponents of this view hold that the TR is the preserved Word of God, and that the modern, scholarly Greek New Testaments are inferior due to their lack of words such as "Christ" in 1 Corinthians 9:1 or "Jesus" in 2 Corinthians 5:18. The KJV, being the most popular English translation from the TR, is held by this group to be the English version of God's preserved Word.
A quick Google search turns up an overwhelming amount of information, mostly blogs. Of the ones the I skimmed, I found this one to be somewhat informative.
In addition to this, I think that it's probably also somewhat of a social phenomenon in that it was the first English translation to really gain mainstream adoption (only slightly younger than the Geneva Bible) and it probably didn't hurt that the primary English-speaking audience of the time were the subjects of the one who commissioned the KJV. So I guess, in addition to the reflective reasons presented presently, it probably "just stuck" within a set of traditions of the Church. People usually like tradition, and as Christians we also like remaining connected to our heritage. The KJV is an important portion of that heritage and may have been unduly venerated.
The KJV has been the 'standard' English translation for a very long time - in fact literally for centuries. It had no real rival for popularity until the publication of the Revised standard Version in 1952. This means that in the early part of the 20th Century a huge number of Christians formulated their doctrine based almost entirely on the KJV.
When the more modern translation became available those who had based their doctrine on the KJV had two choices: revise their doctrine, or decry the new translation as 'false'. Those who took the latter route became the KJV-only movement.
Why is the KJV frequently said to be the “true” translation?
There are basically two reasons for preference of the KJV in regard to accuracy.
The opinion that the Greek manuscripts from which the KJV is derived are superior to the more recently discovered manuscripts (of which the Alexandrian is one of the oldest).
The opinion that newer translations are either intentional or unintentional distortions. Also there can be the associated idea that God has supernaturally preserved the accuracy of his word in the KJV.