Legally I have no idea what the government claims applies or does not, but reading the declaration it seems pretty clear that the founders had the still-radical notion that most/all of these fundamental rights apply to all people ("men", in the text, and "[white] men" in practice). There wasn't even such a thing as "American" when it was written.

If the US thinks the bill of rights should only apply to citizens of the US, the US is morally bankrupt.