I'll bypass your insistence that you know more about the founding principles than John Adams, and get straight to the point.<quoted text>
How about, "The credit goes to Bob and and Sue" being recopied as "The credit goes to Bob"? Does it matter that I didn't say ONLY Bob? It's possible that the author actually credited Sue more.
Adams was giving credit to a variety of sources providing "general principles on which the fathers achieved independence" - Christian, English and American. Changing it to just one misrepresents his beliefs. I happen to believe that Christianity played no part, and Adams doesn't mention specifically what part he thinks it played. He may mean a tiny part. That is for the reader to judge.
But when the other sources are omitted, it appears that Adams meant that Christianity alone provided the principles of which he speaks, which it is assumed was Barton's intent when he deleted the others.
In any even, you can take heed of how this kind of thing is perceived, or just keep insisting that it doesn't matter. It appears that you have little hope of convincing most of us that Barton can be trusted to report facts without distorting them in defense of his thesis. He is tendentious, which Throckmorton addressed:
"The duty of Christians as scholars is first to get the facts correct ... First, scholars labor to uncover the facts about a subject, whether they relate to a historical figure or an aspect of social science. Second, scholars follow the data where they lead. To achieve these objectives, Marsden counsels the Christian scholar to avoid tendentiousness. Tendentiousness might best be described as the kind of argumentation made by lawyers in support of a client where every fact is turned and twisted to be in support of the client. Scholars cannot look like lawyers finding any fact to support their case and excluding or distorting those facts which undermine the case."
This is what the ID scientists are accused of as well.
The fatal flaw in your analogy is that "The credit goes to Bob and and Sue" is not the type of question in play. The question in play is properly analogized as a response to "The credit does not go to Bob"., as in "The founding was not based on Christian principles".
So then, the unearthing of the quotation "The credit goes to Bob..." is perfectly legitimate and proper, on point, and omits nothing relevant to the question.
You have no case.