If you think that is true than you can provide a verse in the KJV that is demonstrably different in the Douay-Rheims.
“One of the sources for the KJV was the Vulgate and the translators of the KJV used the Douay-Rheims to double-check their translations of the New Testament.”
Wiki on DR:
“Much of the text of the 1582/1610 bible, however, employed a densely latinate vocabulary, to the extent of being in places unreadable; and consequently this translation was replaced by a revision undertaken by bishop Richard Challoner; the New Testament in three editions 1749, 1750, and 1752; the Old Testament (minus the Vulgate apocrypha), in 1750. Although retaining the title Douay-Rheims Bible, the Challoner revision was in fact a new version, tending to take as its base text the King James Bible rigorously checked and extensively adjusted for improved readability and consistency with the Clementine edition of the Vulgate.”
http://en.wikipedia.org/wiki/Douay-Rheims_Bible
Wiki on the KJV:
“Instructions were given to the translators that were intended to limit the Puritan influence on this new translation. The Bishop of London added a qualification that the translators would add no marginal notes (which had been an issue in the Geneva Bible). King James cited two passages in the Geneva translation where he found the marginal notes offensive:[25] Exodus 1:17, where the Geneva Bible had commended the example of civil disobedience showed by the Hebrew midwives, and also II Chronicles 15:16, where the Geneva Bible had criticized King Asa for not having executed his idolatrous grandmother, Queen Maachah. Further, the King gave the translators instructions designed to guarantee that the new version would conform to the ecclesiology of the Church of England. Certain Greek and Hebrew words were to be translated in a manner that reflected the traditional usage of the church. For example, old ecclesiastical words such as the word “church” were to be retained and not to be translated as “congregation”. The new translation would reflect the episcopal structure of the Church of England and traditional beliefs about ordained clergy.
James’ instructions included several requirements that kept the new translation familiar to its listeners and readers. The text of the Bishops’ Bible would serve as the primary guide for the translators, and the familiar proper names of the biblical characters would all be retained. If the Bishops’ Bible was deemed problematic in any situation, the translators were permitted to consult other translations from a pre-approved list: the Tyndale Bible, the Coverdale Bible, Matthew’s Bible, the Great Bible, and the Geneva Bible. In addition, later scholars have detected an influence on the Authorized Version from the translations of Taverner’s Bible and the New Testament of the Douay-Rheims Bible.[26] It is for this reason that the flyleaf of most printings of the Authorized Version observes that the text had been “translated out of the original tongues, and with the former translations diligently compared and revised, by His Majesty’s special command.”
http://en.wikipedia.org/wiki/Authorized_King_James_Version#New_version
The comment on the KJV having detected influence - whatever that means - of the DR is supported by page 328 of “Wide as the waters: the story of the English Bible and the revolution it inspired”. Yes, I own the book. No, I cannot find it. When I do, I’ll check out what it says.
However, I don’t think it is accurate to say “the translators of the KJV used the Douay-Rheims to double-check their translations of the New Testament”.