Knowledge of the history of how the A.V. came into print in 1611 is essential to understand why many Christians say it is the most accurate translation available today.
There are two main pedigrees of ancient manuscripts; the NIV and most modern translations use the Alexandrian Text (which led to the RC Latin Vulgate Bible), whilst AV and older translations use the Hebrew Masoretic plus Greek 'Received' texts (The Majority Text). Some Protestants see a Catholic agenda at work with the Catholic preferred text being mainly used today, and I now quote from a leaflet, "Correcting the King James Bible", which should help you understand.
"Correctors of the KJ Bible usually do this on the basis of the Greek texts of Westcott and Hort, Aland and Metzgar or Nestles, which are taken from manuscripts officially approved by the Roman Catholic Church.
"These Roman Catholic Greek texts come from revisions of the Koina (common Greek texts) into the classical Greek texts by the apostate Alexandrian schools in the 3rd and 4th century. The apostate revisors of the Bible who mixed it with heathen philosophy were Hyschius Origen, Pamphilius, and Eusebius.
"When Pope Damasius, the first Pope to take the heathen title Supreme Pontiff, was installed in 380 he commissioned Jerome to revise the Old Latin with these corrupt Alexandrian Egyptian texts...
"In 1475 a corrupt classical Greek Alexandrian manuscript was found in the Popes' library. It was called Codex (book) B Vaticanus.
"In 1587 the Pope put out the Sixtine Edition which used the Vaticanus as its source in order to defeat the Bibles the Protestants and Baptists used which came from the Koina Greek used by the Apostles. In the 19th century a Catholic movement in the Anglican Church resulted in an English Greek put out by two English Anglican Catholics who believed in Mary worship, named Westcott and Hort. Their text was based primarily on the corrupt Vaticanus manuscript which has readings found in no other manuscript in the world..."
The work of translating the AV was assigned to six reputable groups of qualified scholars. They knew and used Greek and Hebrew manuscripts to determine the best meaning of words for the Shakespearian English of their day. This meant that the resulting King James Bible was not based on Latin, but on the languages that the Bible had originally been written in. They worked from the Masoretic Text of the Old Testament, and the Textus Receptus family of the Greek New Testament (which is known as “The Received Text”).
This followed the early printed editions of Desiderius Erasmus of Rotterdam (1469? – 1536), a Roman Catholic humanist who translated the New Testament into Latin and prepared an edition of the Greek to be printed beside his Latin version to demonstrate the text from which his Latin came. Erasmus used six or seven Greek manuscripts, the oldest being from the 10th century. His edition was published in 1516. There was also the Greek NT published by the Elzevirs in 1633. In its preface, it contained the Latin phrase “textum... receptum” so it became known as “the Textus Receptus” or, the Received Text. It included other editions of the Greek NT that come from the same Byzantine textual family, representing the majority of the handwritten Greek manuscripts before the 16th century. The work of William Tyndale was also greatly used.
But the Alexandrian pedigree certainly seems to have opened the door to liberties being taken in modern Bibles, which has not happened with the Textus Receptus.