Because it's not a fallacy. The Framers -- all of them (including the deists, Franklin and Jefferson, notwithstanding their attraction to Enlightenment perspectives [Jefferson was in Paris at the time of the Philadelphia Convention, but had been able to correspond]) -- were firmly planted in the Judeo-Christian world view. You have only to listen to them speak, in their writings, to know that.
That is to say, they believed in God, the creator of the world and of man; that God "created all men equal," vesting in them reason and free will; and that God is the source of men's inalienable rights to life, liberty, and property (or "happiness").
To doubt this is tantamount to saying Jefferson was a crafty, calculating liar when he penned the DoI, that this key document is a tissue of lies....
These insights motivated the Framers' desire to create a system of ordered liberty and equal justice under law; for nothing else would be appropriate to God-given human dignity.
Further, they clearly believed that the Ten Commandments and the Two Great Laws of the Christian dispensation were divinely communicated to man, and that they were, in fact, the moral law designed by God to serve mankind, according suitably to his divinely created nature. These ideas are implicit in the philosophy of the Constitution itself.
But if you want to engage in revisionist history, don't let me stop you. You wouldn't be the first, or the last.