Did makers of the KJV borrow from 1582 Rheims or did they translate the same way?

In another thread,

Are all the scholars who have examined the evidence and who concluded the same thing as I have based on that evidence incorrect?

In his introduction to a modern-spelling edition of Tyndale's New Testament, David Daniell noted:
When James I gave his Bible revisers the huge
Bishops' Bible as their foundation, which meant
that the Vulgate-based Rheims version would be
attractive to them, he ensured that a wash of Latinity
would be spread over Tyndale's English. The
result, and we must assume, the intention, was to
create a safer distance between the Scriptures and
the people. Though in the general working vocabulary
there were more Latinate terms in use by 1611, Latin
words and constructions have, as they had then, the
ring of Establishment authority, which is not the same
as the Koine Greek that Tyndale was translating for the
first time (p. xxiv).
Daniell wrote: "For King James to lay down as the foundation of his new version the most Latinate of recent indigenous Bibles was unfortunate indeed, and destroyed the chance of the new version being in the best modern English" (p. xiii). Daniell wrote: "Another, more serious, push toward Latinity came from the influence on the [KJV] panels of the extremely Latinate Roman Catholic translation from Rheims" (Tyndale's N. T., p. xiii).

David Norton asserted that “Rheims’s prime contribution to the KJB was an added sprinkle of latinate vocabulary in the NT” (KJB: a Short History, p. 32).

Charles Butterworth noted: "There are instances where the Rheims New Testament reads differently from all the preceding versions and yet has been followed later by similar readings in the King James Bible, indicating that the translators of 1611 by no means ignored the work that was done in 1582" (Literary Lineage of the KJV, p. 195).

Darlow and Moule wrote: “This Rheims New Testament exerted a very considerable influence on the version of 1611, transmitting to it not only an extensive vocabulary, but also numerous distinctive phrases and turns of expression” (Historical Catalogue, p. 96). Darlow and Moule noted that “the Rheims New Testament, though not mentioned--contributed appreciably to the changes introduced” (p. 134).

John R. Kohlenberger III observed: “Although Bancroft did not list the Catholic Rheims (1582) translation of the New Testament as a resource to be used, and although Miles Smith does not cite it by name, the translators occasionally followed its readings” (Burke, Translation That Openeth the Window, p. 47).

J. R. Dore wrote: "A very considerable number of the Rhemish renderings, which they introduced for the first time, were adopted by the revisers of King James's Bible of 1611" (Old Bibles, p. 303).

Herbert May confirmed that "some of its [the Rheims] phrases were used by the King James Version translators" (Our English Bible in the Making, p. 47). In his 1808 answer to the reprinting of Ward’s 1688 book Errata of the Protestant Bible, Edward Ryan referred to the KJV translators “adopting the Romish Version in very many instances” and to their making corrections “agreeably to the popish construction“ (Analysis, pp. 5-6). Benson Bobrick also observed; "From the Rheims New Testament, the translators saw fit to borrow a number of Latinate words" (Wide as the Waters, p. 244). Samuel Fisk also acknowledged that the Rheims had "an influence upon the King James Version" (Calvinistic Paths, p. 74).

James Carleton noted: "One cannot but be struck by the large number of words which have come into the Authorized Version from the Vulgate through the medium of the Rhemish New Testament" (Part of Rheims in the Making of the English Bible, p. 32). In his book, Carleton gave charts or comparisons in which he gave the rendering of the early Bibles and then the different rendering of the Rheims and KJV.

In the introductory articles in Hendrickson’s reprint of the 1611, Alfred Pollard maintained that “the exiled Jesuit, Gregory Martin, must be recognized as one of the builders of the [1611] version of the Bible” (p. 28). David Norton affirmed that the words borrowed from the Rheims “make Martin a drafter of the KJB” (KJB: a short History, p. 32). Norton added: “Since most of them are transliterations of Jerome’s Latin, they also make Jerome an author of the KJB” (Ibid.). Norton pointed out that “the Roman Catholic John Hingham (fl. 1639) was to claim that the KJB in fact supported Roman Catholic, not Protestant views” (History, p. 54).

It is most likely that the KJV translators obtained their knowledge of the Rheims New Testament from a book by William Fulke which compared the Rheims N. T. side by side with the Bishops'. In his introduction to a 1911 facsimile reprint of the 1611, A. W. Pollard maintained that "probably every reviser of the New Testament for the edition of 1611" possessed a copy of Fulke's book that "was regarded as a standard work on the Protestant side" (p. 23). John Greider observed that “This work [by Fulke] was studied by the translators of the 1611 Bible” (English Bible Translations, p. 316). Peter Thuesen pointed out: “William Fulke’s popular 1589 annotated edition of the Rheims New Testament, though intended as an antidote to popery, in reality had served as the vehicle by which some of the Rhemists’ Latinisms entered the vocabulary of the King James Bible” (In Discordance, p. 62). David Norton noted that KJV translator William Branthwaite had a copy of “Fulke’s parallel edition of the Rheims and Bishops” in his personal library (KJB: Short History, p. 64). Norton also pointed out that the Bodleian Library in 1605 had a copy of Fulke’s edition of the Rheims and Bishops’ New Testaments (Ibid.).

W. F. Moulton stated: "The Rhemish Testament was not even named in the instructions furnished to the translators, but it has left its mark on every page of their work" (History of the English Bible, p. 207). Diarmaid MacCulloch and Elizabeth Solopova asserted that in the KJV “it was possible to see some of the readings of the Doua-Rheims version amid all the work of Tyndale, Coverdale and the Geneva translators” (Moore, Manifold Greatness, p. 38).

Ward Allen maintained that "the Rheims New Testament furnished to the Synoptic Gospels and Epistles in the A. V. as many revised readings as any other version" (Translating the N. T. Epistles, p. xxv). Allen and Jacobs claimed that the KJV translators "in revising the text of the synoptic Gospels in the Bishops' Bible, owe about one-fourth of their revisions, each, to the Genevan and Rheims New Testaments" (Coming of the King James Gospels, p. 29). About 1 Peter 1:20, Allen noted: “The A. V. shows most markedly here the influence of the Rheims Bible, from which it adopts the verb in composition, the reference of the adverbial modifier to the predicate, the verb manifest, and the prepositional phrase for you” (Translating for King James, p. 18). Concerning 1 Peter 4:9, Allen suggested that “this translation in the A. V. joins the first part of the sentence from the Rheims Bible to the final phrase of the Protestant translations” (p. 30). Ward Allen observed: "At Col. 2:18, he [KJV translator John Bois] explains that the [KJV] translators were relying upon the example of the Rheims Bible" (pp. 10, 62-63). The note of John Bois cited a rendering from the 1582 Rheims [“willing in humility”] and then cited the margin of the Rheims [“willfull, or selfwilled in voluntary religion”] (p. 63). Was the KJV’s rendering “voluntary” borrowed from the margin of the 1582 Rheims? Thus, the first-hand testimony of a KJV translator acknowledged or confirmed that the KJV was influenced by and followed the example of the Rheims.

 

How could the makers of the KJV and the makers of the 1582 Rheims New Testament be translating the same text the same way?

The makers of the KJV claimed to be translating from the Greek New Testament as their standard while the makers of the 1582 Rheims New Testament claimed to be translating from the Latin Vulgate as their standard text.