As an American, I do not believe rights come from any Creator or from nature. Additionally, I can give a logical argument why they don't:
1. Throughout the vast majority of history, the idea that rights come from any Creator or Nature did not exist. That was a philosophy that arose during The Enlightenment, specifically John Locke's Second Treatise, which our Founding Fathers were part of.
Tell me something, do you believe slavery was a violation of rights? How bout the denial of the vote to women for so long? At the time those things were going on, the government didn't recognize the rights of African Americans or the right of women to vote. Under the logic that rights only come government, since the government didn't recognize those rights, we would have to conclude that slavery did not violate any rights, nor did the denial of the vote to women. Unless, rights are more complicated than just what the government does and does not recognize.
2. Throughout history, it was a governing body of people or a governing person that exclusively granted any 'rights' to any members of society, be that a monarch, Parliament, Congress, or Council.
If rights come from those entities, it follows they can be taken away from those entities. It would also follow that those entities could never be guilty of violating your rights. After all the rights only come from them and therefor if they say you don't have the rights, you don't. Right? Unless rights are something more complicated than whether or not a given government recognizes them.
3. Do you see the Law of Nature or a Creator giving those 'rights' to North Koreans, the Chinese, the Russians, or the Cubans?
I believe the Chinese, Russians, and Cubans have certain inalienable rights and that their governments are violating their rights. Or do you think their rights are not being violated?
Give me a logical reason or piece of evidence that "rights" come from nature or a Creator.
As I said above if they rights only given to us by government, we can't complain when they take those rights away. They can simply say to us, "you only have what rights we tell you have".
No, it is a declaration of independence. The title is a hint. The rest is a justification for that based on their beliefs. "Look! God and Nature are on our side!"
It is a declaration of the idea that rights do not come from the King, they are above the King, and the King was violating those rights and therefore we justified our revolution.
Our whole revolution and country is based on the idea that rights do not come at the mercy of government, or the king, they come from above, from a creator or nature. If the government fails to recognize those rights, it is the right of the government to change such government.
If nature and a Creator give rights, then why did the writers of the Constitution need to spell them out in a legal document? Take the supernatural and a personified "Nature" out of it and the Constitution would be just as legal and effective.
As I have said previously, some of the founders didn't like the idea of spelling them out in the Bill of rights, they were concerned it would like they were coming from the government and not the creator or nature. But others wanted them spelled out.