You have to be careful mixing and matching bits and pieces of philosophy from different groups of people in different time periods. The framers did talk about natural rights, but you need look no further than their interactions with the American Indians to understand that when they talked about "natural rights" they were more referring to rights inherent to Englishmen than rights common to all humans. To put it glibly, do you think the framers would have objected to using drones against the American Indian threat?
> 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.
> 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.