Okay, after this post noting that parts of the PBS special (which I haven't yet seen -- when is it going to be broadcast?) perhaps look fair, Ed Brayton posts on something biased. Brayton quotes the the narration:
"The United States is a society based on the rule of law. And our Founding Fathers believed that if they did not base their laws on a higher authority, then whoever was in power would determine what the law said. They called this `tyranny.' Their higher authority was the Law of God - the Ten Commandments."
This fundamentally misrepresents the Founders' notion of "higher law." Yes, even though the Constitution does not invoke a higher law, the Founders, I'd argue, did believe in such because the Declaration invokes higher law. But, as I noted here, that higher law was not -- or predominantly not --revelation, but reason.
Our Founders who wrote the Declaration -- Adams, Jefferson, and Franklin -- believed only revelation which could meet the test of reason was part of that "higher law." Those three believed the Trinity flunked such test and hence wasn't part of that higher law. And the Ten Commandments -- as a whole -- couldn't meet that test either. Both Jefferson and Adams doubted the Ten Commandments were legitimately revealed. As Jefferson wrote to Adams in 1824:
Where did we get the ten commandments? [The Bible] itself tells us they were written by the finger of God on tables of stone, which were destroyed by Moses; it specified those on the second set of tables in different form and substance, but still without saying how the other were recovered. But the whole history of these books is so defective and doubtful, that it seems vain to attempt minute inquiry into it; and such tricks have been played with their text, and with the other texts of other books relating to them, that we have a right from the cause to entertain much doubt what parts of them are genuine.
And as Adams wrote to Jefferson Nov. 14, 1813:
When and where originated our Ten Commandments? The Tables and The Ark were lost. Authentic copies, in few, if any hands; the ten Precepts could not be observed, and were little remembered.
If the Book of Deuteronomy was compiled, during of after the Babilonian Captivity, from Traditions, the Error or Amendment might come in there.
So, the "Nature's God" who grants men natural rights is not necessarily the God of the Bible (but perhaps is). Consider, that higher law which no man made law can contradict grants men the unalienable right to break the first tablet of the Ten Commandments. Though they disagreed on proper establishment policy, all of the key Founders -- Washington, Adams, Jefferson, Madison, Franklin, et al. -- believed men of all religions had the unalienable right to worship as they chose. So whereas the God of Scripture, in the very first command, forbids the worship of any false gods, the Founders' Nature's God grants men an unalienable right to worship no God or false gods.
When the Ten Commandments were incorporated in the pre-Founding colonial civil laws, the results were laws meriting the death penalty for worshipping "any God but the lord God." Contrast that with the Founding Fathers debating Church/State law in VA. George Washington, arguing contra Jefferson and Madison, noted he believed it fine to use tax dollars to support teachers of the Christian religion provided folks who "declare[d] themselves Jews, Mahomitans or otherwise, [could] thereby obtain proper relief." If we were back in colonial VA or MA (most colonies I believe) folks who declared themselves Muslims or Jews, or non-Christians would be facing execution (or if lucky, banishment) because they publicly declared themselves breakers of the First Command (and no, back then the fundamentalist Churches did not believed that Jews, Christians, and Muslims worshipped the same God; to them, if you weren't Trinitarian, you worshipped a false God).
In sum, if the higher law grants all men unalienable rights of conscience, to worship as they please -- and all key Founders believed it did -- it is impossible that the Ten Commandments, as a whole, are part of the "higher law" which no man made law can contradict.