The translators say in their preface that they had not seen all of the Catholic bible. Besides, anyone who has read Bible history knows that the KJV was based on Tyndale's GREEK tests from Eurasmus and not the LATIN based Douai Rhemes.
From the Translators to the Reader 1611 KJV
Now to the latter we answer; that we do not deny, nay we affirm and avow, that the very meanest translation of the Bible in English, set forth by men of our profession, (for we have seen none of theirs of the whole Bible as yet) containeth the word of God, nay, is the word of God. As the King's speech, which he uttereth in Parliament, being translated into French, Dutch, Italian, and Latin, is still the King's speech, though it be not interpreted by every Translator with the like grace, nor peradventure so fitly for phrase, nor so expressly for sense, everywhere.
As for the “missing “ books, the original KJV had them in it. Many considered them irrelivant and they were removed about the time the Americans started printing bibles.
Here is a list of the translators and you can see there was a committee to translate the Apocrypha.
KING JAMES VERSION TRANSLATORS
I. The First Westminister Company—translated the historical books, beginning with Genesis and ending with the Second Book of Kings.
Dr. Lancelot Andrews
Dr. John Overall
Dr. Hadrian Saravia
Dr. Richard Clarke, Dr. John Laifield, Dr. Robert Tighe, Francis Burleigh, Geoffry King, Richard Thompson
Dr. William Bedwell
II. The Cambridge Company—translated Chronicles to the end of the Song of Songs.
Edward Lively, Dr. John Richardson, Dr. Lawrence Chaderton
Francis Dillingham, Dr. Roger Andrews, Thomas Harrison, Dr. Robert Spaulding, Dr. Andrew Bing
III. The Oxford Company—translated beginning of Isaiah to the end of the Old Testament.
Dr. John Harding, Dr. John Reynolds
Dr. Thomas Holland, Dr. Richard Kilby
Dr. Miles Smith, Dr. Richard Brett, Daniel Fairclough
IV. The Second Oxford Company—translated the four Gospels, the Acts of the Apostles, and the Revelation of St. John the Divine.
Dr. Thomas Ravis, Dr. George Abbot
Dr. Richard Eedes, Dr. Giles Tomson, Sir Henry Savile
Dr. John Peryn, Dr. Ralph Ravens, Dr. John Harmar
V. The Fifth Company of Translators at Westminster—translated all of the Epistles of the New Testament
Dr. William Barlow, Dr. John Spencer, Dr. Roger Fenton, Dr. Ralph Hutchinson, William Dakins, Michael Rabbet, [Thomas(?)] Sanderson
VI. The Sixth Company of Translators at Cambridge translated the apocryphal books.
Dr. John Duport, Dr. William Brainthwaite, Dr. Jeremiah Radcliffe
Dr. Samuel Ward
Dr. Andrew Downes, John Bois
Dr. John Ward, Dr. John Aglionby, Dr. Leonard Hutten
Dr. Thomas Bilson, Dr. Richard Bancroft
The King James translators did not consider Apocrypha scripture—
Yeah thats right there have been at least three different versions of the 1611. Lets be aware of one important facts the "translators can say what ever they like, but it has been documented that significant portions of the King Jimmy have been lifted directly from the D/R.