The basic idea though, is do we want to appeal to a higher authority than men for what are basic human rights.
There seems a certain logic, as has been suggested on this thread, to the idea that rights stand or fall on the authority of the legal system behind them. History suggests the "fall" part has happened before, or in lesser ways in the US by the rising and falling of interest groups.
In a sense at least, the Bible seems to concur. The Ten Commandments begin with a demand to recognize the authority of the God of the patriarchs and of the Exodus events. And Jesus tells His disciples to tell their disciples to "observe everything I have commanded you." Law, and hence any rights derived from law, is only as good as the law-giver and the "social contract" with the law-giver.
What I tried to argue in part in a previous post to this thread is that despite confusion, there exists certain universal and absolute ethical principles (and hence rights) based on the authority of the God who created and sustains everything. These principles, because universal in God's world, may be recognized by and written into the legal systems of the nations, so that appeal to these laws and rights without respect to God is sometimes made.
But note that appeal to such rights would be unnecessary if there were no violations of God's universal laws. Then what might appeal to those rights as coming from God accomplish (assuming those rights are correctly defined and do come from God)? And what would be the intent?
Such appeal will not, for example, change human nature and human violations of absolute ethical principle--will not even change all distortions of claims of right and wrong. God has revealed Himself and what is right and wrong to all persons, yet often we "suppress the truth in unrighteousness" (Rom. 1). We humans often deceive ourselves to the point of not acknowledging God and His laws.
Thus appeal to rights as coming from God may or may not have the (presumably) desired effect of correcting behavior in human court or elsewhere. Such appeal may nonetheless serve as witness against wrong-doers that in His own time and way, God will enforce His law. Such appeal may be particularly warranted where pressure is brought to bear for doing wrong, "I have a right not to do wrong." At other times it may be advisable not to insist on one's rights at all, such as to exercise patience or submit to unjust suffering for the sake of the gospel.
I would close again with caution, however, that right and wrong be carefully defined and identified with God. As has been said on this thread already, there are claims to divine origin of "rights" which ain't so. Other rights are specific to a human legal system, but bear perhaps at most only tangential relationship to absolute and universal ethical principle.