I think they drop the ball when they start claiming Locke and others like Ben Franklin as secret atheists. Still, there is something to the notion that when orthodoxy is enforced at the point of a gun either literally or metaphorically, the heterodox will speak in code to avoid facing the music.
Still, I think it's important to claim only that esoterism for which there is solid evidence. I see, among the notable, relevant figures I chiefly study, more solid evidence of hushed up theistic heterodoxy than secret atheism. I also see more public generic God words that could mean more than one thing to one person than blatant public lying.
So when Thomas Jefferson, as a public statesman, indeed as 3rd President of the United States, spoke publicly of "Providence," he could esoterically mean something unitary (in which he truly did devoutly, personally believe) that might convey "Triune" meaning to an orthodox listener who wished to "read that in." When Washington used "Providence" (his favorite God word), we really aren't sure what he meant; though I strongly suspect he meant something unitary.
The exoteric God words are generic. And the generic approach permits honesty of personal conviction. Such terms are compatible with secret heterodox esoteric meaning and a more orthodox meaning entrenched forces attempting to control public institutions might wish to read in.
Ezra Stiles, notable patriotic preacher of America's Founding era, President of Yale, and personal friend to many of America's "key Founders," was one of the few who later explicitly detailed his secret beliefs in "non-respectable" positions that could have earlier ruined his career and standing in "respectable" society.
It seems though, rather than beat around an esoteric bush, often times he just lied. In 1751, believed to be near death and from which he would recover, Stiles gave an orthodox confession to an orthodox confessor while later admitting that not only did he NOT believe Christianity was "divine" at that time, but had never told another human being of his secret "infidelity." Keep in mind, Stiles was
Stiles was a notable, perhaps even a "key" player during America's Founding era. Arguably, he typified the revolutionary-republican, "Whig" political thought and its theology. And his life -- his words and deeds -- makes us question whether that theology and thought meaningfully accords with or derives from traditional orthodox biblical Christianity at all.