Recognition of and respect for human rights need not be bound to sovereign freedom of action, as you put it. Freedom of action does not have to imply freedom to coerce.
And for myself, I don't like to argue in terms of any sort of thing, "natural rights" or "God's law" or whatever, that a doctor couldn't find if he cut me open and poked around. To me, the ability to act is the only thing that exists, and "rights" are just people in a community agreeing to use collective force to enforce whatever they decide to call "rights." The idea that the community as a whole can be bound to limit its ability to act with respect to people outside that compact is to me not a sensible thing.
And I think that while most Americans wouldn't phrase it precisely in that way, their thinking is along similar lines. We're a country that strenuously reserves the right to do whatever the hell we want, bound only by our own collective conscience. We want to do right by people, but we get to be the final arbiters of what's right and what is justified.
The folks who architected this nation most certainly did, and since they're the ones who devised the sovereignty of the states and embodied the individualism and self-reliance and runs undercurrent to your claim that Americans "hate the idea of being obligated or beholden to anyone else" I think it's perfectly fair to characterize the debate in those terms. And they did in fact see these as universal rights: "We hold these truths to be self-evident, that all men are created equal..."
Anyways, specifically I take issue with your claim that "the idea of "human citizen[ship]" is anathama to American thought, because citizenship implies reciprocal rights and obligations." Obligations, yes, but it does not follow that the extension of our recognized rights to all people is in any way contradictory to our ideals, your personal views on collective rights notwithstanding.
> but it does not follow that the extension of our recognized rights to all people is in any way contradictory to our ideals
No matter what theory of the nature of rights you subscribe to, as a practical matter "rights" are limits on collective action. To say that, say, a non-American in Yemen has "rights" is to say that there are things that the American people, acting through Congress, cannot do. That is what is inconsistent with Americans' perceptions of the world. Not because we think people in Yemen are a lesser sort of human, but because Americans don't accept the idea that there is some higher power that can decide what America can and cannot do.