As I read these stories, I was reminded of the stories of German almost becoming the official language of the US instead of English, in that it seems that there are many false stories about the early congress. However, in every case, it seems, the problem is, as Rodda puts it, “It tells half of the real story, includes a quote from an actual committee report, but ends with a fabricated resolution.”
I conject that these lies persist because they point to real documents (“Surely no-one would lie about something so checkable?”) that are rather dense and difficult to read. (Just take a look, here is page 334 of the Continental Congress's papers.) The language is closer to the Early Modern English of Shakespeare than it is to the way we speak today (A fact that is highlighted by the issues surrounding saturday next.), and the written style is a kind of script that is never used any more. You can take classes in how to read this kind of stuff at a university's history, linguistics, and English departments, or you can slog through it, but the liars know that most people will not bother to do so. And of course, the lies of record omission can be bolstered if there are people like Aitken who were willing to stretch the truth even at that time. All you have to do is use a couple of careful official quotes and then let Aitken's lies come through to today.
Unfortunately, this type of lie can remain very effective even if someone does go back and look up what's going on. Reading the committee report without the surrounding information, it seems to back up that congress was worried about a lack of bibles; reading the redacted resolution on the Aitken bible, it is easy to be mislead and think that congress was supporting religion (and not the book industry); and if you look at the title, and not the content, of the various post-constitution acts, it is easy to think that congress was enamoured of religion when in fact it was simply assisting people. Given the difficulty in getting through the source material, who is going to go around in the other papers looking for evidence that what they've seen is not the full story? (Well, a historian would, but let us be realistic about how much time the average person has to devote to something like this.) This is the scary thing about quote-mined, carefully reworded lies. These lies take time and effort to debunk and destroy.