Rights come from government.
It's a pretty simple concept.
You're equivocating between existential freedom and government protected rights. The concepts are related, but not at all the same thing.
Whether government protects a given natural right has no bearing on whether the right exists. The question is whether someone can expect government to protect it or not. It's not a simple concept, but neither is it terribly subtle. Natural rights are existential freedoms that we have as a result of having volition.
The question is, which of these rights should government protect? It was the, literally revolutionary, notion of the framers that government should strive to protect freedom as a general principle. Which is what I believe TJ was trying to get across in the preamble to the declaration. The natural rights angle was his way of turning the tables on the prevailing view (which, sadly, many people here seem to share) that any freedoms we might enjoy are favors granted to us by authority (then the king, today the federal government).