"Those who believe in the origins of the law don't rely on their own fallible opinion."
The "Infallible." source you refer to so often results in disagreements on the details of implementation as to have resulted in one major split, one major schism and hundreds of variations some of which have even added more books in the last 200 years.
So, even if you consider it infallible, people are not, and it is people that implement the law. Therefore for a government to sanction a law and suggest that it is from an infallible source which therefore precludes questioning it's validity and then to implement it with inevitable human failings is dangerous and more appropriate to dictatorial regimes than a democratic republic.
I am not suggesting the government take a religious belief or advocate a religious position. I am suggesting that our founding documents (of which the Declaration of Independence is one) recognize God's natural law as foundational to our legal structure. What you find in the Bill of Rights aren't a list of rights we are allowed by the government but strictly imposed limits on the government from infringing on our God-given rights. Read the Declaration and the Federalist Papers and you will see that was the intent.
God is the grantor of rights; government is the taker. (Hey! New tagline!) That is the legal reasoning behind the Constitution.