[TheRealThing]

If the reasoning put forth, then, is that "God's law" is higher, and, therefore, all are subject to it, and that is applied in the civil government plane, how is that different from the reasoning behind sharia?

Uh, could it possibly be it is different because God is alive and sovereign as compared to all of the fictional gods? And that all men are subject to it (God's law) because God has clearly stated exactly that? That being the case, nobody has ever said the US is a theocracy. Governing a nation is a completely different issue than defining moral issues. And yet governing with His sovereignty in mind only makes good sense if we want to avoid the pitfalls of moral error, and if we expect to lay rightful and indisputable claim to the moral authority under which we govern.