The Constitution does talk about inalienable rights, specifically in the 5th and 14th Amendments. Life, liberty and property to be exact.
Exactly. And where do these "inalienable" rights come from? The Declaration of Independence explains it: they are given by God to every human person, and cannot be taken away by any just government.
The Constitution does not give inalienable rights--or they wouldn't be truly inalienable. It recognizes their existence.
The Constitution, Like the Declaration, was based on Natural Law theory. Many people, I think rightly, consider the Declaration of Independence to be one of the foundational documents, a kind of preamble that helps to explain what certain words and phrases mean in the Constitution.
Certainly that makes more sense than to try to explain "freedom of religion" in the Bill of Rights as what amounts to freedom from religion, a "wall of separation between church and state. As SCOTUS did when it outlawed God and the Bible in our public schools.
Not to overlook each item in the (original) Bill o'Rights, which the author of the DOL is mostly responsible for having inserted into the Constitution when other Founders thought that the original document would suffice.
Palin is correct when stating that our Constitution does indeed grant the citizens of the U.S. inalienable rights, as defined in the DOL. She did not state that the phrase "inalienable rights" was to be found in the Constitution.
That stated, the two documents go hand in hand. Without the DOL, the Constitution would not have been created.
So, no, it bothered me none the least when she, or anyone else, speaks of 'inalienable rights' and our 'Constitution'.