From what I can tell, these theological unitarians believed in direct revelation in a God speaking to man sense; but I also see them as skeptical towards the infallibility of the biblical canon. Hence Adams' lauding their "biblical criticism." They weren't trying to "debunk" the Bible like an atheist or strict deist would. Rather, clarify the proper understanding by removing the errors.
With that, see this post by a traditional conservative Christian entitled Belsham’s Unitarian New Testament (1808) which criticizes what Thomas Belsham did to the Bible. Belsham is one of those Unitarians to whom Adams referred.
... Though not yet formulated as an article of faith, reason was even then accepted in practice as the highest tribunal of human appeal.” 9 In a book published in 1798, Belsham indicated his awareness of the incompatibility of the New Testament with Unitarianism by arguing, just as Ellis did later, that not everything in the Bible is inspired, true, and authoritative. “The scriptures,” he wrote, “contain a faithful and credible account of the christian doctrine which is the true word of God: but they are not themselves the word of God, nor do they ever assume that title: and it is highly improper to speak of them as such, as it leads inattentive readers to suppose they were written under a plenary inspiration to which they make no pretension, and as such expressions expose christianity unnecessarily to the cavils of unbelievers.” 10
In line with this critical attitude toward the Bible, we find that the Introduction of the “Improved” version (section 2) refuses to grant the canonicity of some books of the New Testament (Hebrews, James, 2nd Peter, 2nd and 3rd John, Jude, and the Revelation), and its editors even deny that there can be a final and authoritative determination of the limits of the canon. ...