At least in the context of this essay this point seems moot to me. Whether the author argues that only Christianity provided such theories or not, the vast majority of the US founders cite the Christian God as the source of a lot of things, human rights among them. They don’t cite some Greek philosopher because that’s not what they pulled that aspect of their argument from.
Maybe this is just more cut snd dry for me because I’ve studied US history for years and I’m imposing a lot of that into the essay, but I don’t think the author is being disingenuous at all for rightly pointing out the reaching effect of Christianity on our modern understanding of human rights (see Locke’s “Reasonableness of Christianity” for some fun reading).