whose idea was it anyway

William Smith suggested that the inspiration to go to the Bible for determining which denomination to follow was not necessarily one that Joseph Smith Jr had on his own, but may have come from a sermon that William heard about.

... the next evening a Rev. Mr. Lane of the Methodists preached a sermon on “what church shall I join?” And the burden of his discourse was to ask God, using as a text, “If any man lack wisdom let him ask of God who giveth to all men liberally.”16  (Marquardt & Walters, p.20)

The main part missing is the "upbraideth not" that seemed very important to Joseph Smith Jr. Smith Jr recounted himself as reading it (almost like St Augustine):

“While I was laboring under the extreme difficulties caused by the contests of these parties of religionists, I was one day reading the Epistle of James, first chapter and fifth verse, which reads: If any of you lack wisdom, let him ask of God, that giveth to all men liberally, and upbraideth not; and it shall be given him.” (from the LDS website)

Footnote 16 reads:

Interview of William Smith by E. C. Briggs as reported by J. W. Petersen to Zion’s Ensign 5 (13 Jan. 1894): 6, Independence, Missouri; see also, with minor inaccuracies, Deseret Evening News 27 (20 Jan. 1894): 11; Latter-day Saints’ Millennial Star 56 (26 Feb. 1894): 133-34; Church News, 16 [p.37]Mar. 1968, 11. William stated that “Hyrum, Samuel, Katharine [Sophronia] and mother were members of the Presbyterian church” (Zion’s Ensign 5:6), which he described as the “Church, of whome the Rev. Mr. Stoc[k]ton was the Presiding Paster” (William Smith, “Notes Written on `Chamber’s Life of Joseph Smith’ by William Smith,” typescript, 18, LDS archives).
The fact that the names of Smith’s mother and brothers appear later as members of the Palmyra Presbyterian church who were dropped for nonattendance is further evidence that the revival Smith had in view affected the local Presbyterian church. See Western Presbyterian Church of Palmyra, “Session Records,” 2:11-12. Volume 1, which would have shown the exact date the Smiths joined, has been missing since at least 1932.