Let's use some common sense and honesty in assessing Carson's statement about the political inexperience of the DOI signers. The context was that he was discussing career Washington politicians and was contrasting their years of experience with his lack of political experience.
So it seems fairly obvious that he was thinking of national-level experience along the lines of the career politicians that we now have, not state and local legislative experience. And in that sense, his point is perfectly valid.
What's more, if you look at the DOI signers who had held elected office, most of them had been elected to those offices in the fairly recent past, while some others had not held elected office for several years.
And, of course, back then there was no such thing as the kind of national-level experience that one gets as a U.S. senator or representative. The possibility for such experience simply did not exist yet.
The few Continental Congresses that were held were intermittent and only dealt with a narrow range of issues (mainly in relation to responding to various British laws).
Furthermore, nearly half of the DOI signers had never held elected office up to that time.
Was Carson's comment technically in error? Yes, since a little over half of the DOI signers had some elected political experience by that time.
But the thrust, the main idea, behind Carson's comment was correct, i.e., the idea that the DOI signers would be viewed as inexperienced and unqualified for the presidency by many people in our day. And, again, I think Carson was thinking of federal/national-level experience, not state and local experience.