I think Adams thought more highly of the Old Testament narrative than Thomas Jefferson who arguably appreciated little more than the "Deism" of the Jews (their belief in one God). (Though in one of his inaugural addresses Jefferson spoke as though he believed the Old Testament story of God liberating the Jews from Egypt were true.)
Still, because according to Adams, the original Hebrew was destroyed, man could never be sure when reading texts whose original was Hebrew, whether he was reading God speaking to man in the form of direct special revelation or some kind of corruption in the form of interpolation, intermixture, error, amendment, (terms he used).
Likewise, Adams concludes all of St. Paul's writings were originally in Hebrew (because Paul was illiterate in Greek), and thus destroyed, and consequently suspect. Below is an excerpt from Adams' Marginalia, Memoirs of the Life and Writings of Arthur Ashley Sykes, D.D.
Why has the Hebrew been destroyed and lost?
How can they object? When the Hebrew is destroyed? [...]
A resolute Faith! Dr. Disney! If St. Paul ever wrote anything in Greek except his name and a concluding sentence or two, the most eminent Fathers are not competent witnesses.
Does the burden of proof rest upon the infidel to prove a negative? The believer, the assenter, should prove his affirmation.
This is the most candid and the most plausible opinion.* But the question recurs, why was the original destroyed? What suspicions of interpolation and indeed of fabrication might be confuted if we had the originals? In an age or in ages when fraud, forgery and perjury were considered as lawful means of propagating truth by philosophers, legislators and theologians, what may not be suspected?
What was not received? Anything, everything, and nothing.
Why has the original Hebrew been annihilated?
And who were these "Οι αρχαιοι?
And he might as well add Chateaubriand in 1814. And the whole Acta Sanctorum. When Homsousianity was established and Christianity totally corrupted, no doubt, authorities enough might be accumulated.
Upon what authority? Paul's own epistles. But is not this begging the question?
Pray! Which are St. Paul's undoubted epistles?
Is it not strange that these most learned and candid of men, as I believe them to have been, should not agree when they both take the epistles themselves for undoubted authorities?* The context of this entire passage is that Adams is talking to a book -- "Memoirs of the Life and Writings of Arthur Ashley Sykes, D.D." -- and it involves a dialog between Arthur Sykes and John Disney. The "candid" and "plausible" opinion was Disney citing an earlier authority asserting that Paul originally wrote the Hebrew Epistle in Hebrew, but that it was later translated into Greek by another author. That's when Adams notes that in the absence of the originals in Hebrew, which have been lost, it's all suspect. Likewise, Paul if he was the original author, must have written it in Hebrew because he was illiterate in Greek.
See Zoltan Haraszti, "John Adams and the Prophets of Progress," pp. 296-97.