Well this was really just a sub-argument about whether 'inalienable' is an Americanism, which it is. The real point about 'natural' rights, or whatever term you've switched to using, is that they're simply assertions. Not supported by anything else. Doesn't really matter who is asserting them. The argument takes the same form, and is equally bunk.
"Natural rights are those that are not dependent on the laws or customs of any particular culture or government, and so are universal, fundamental and inalienable..."