The assertion of the US' founders is that such rights are inherent to all people, natural rights, and inalienable.
The fact that it was codified into law in a specific country is an implementation detail. The concepts of liberty in the US documents are philosophical assertions and not related to any nation.
They also happen to be law in the US, but even there they don't really hold force; such "rights" are violated constantly.
Nothing of the ideology seemingly professed by the famous US founding set were ever actually implemented. Slavery is just the big obvious one but there are a million other examples of their failure to actually implement their espoused philosophy.
It seems like more of an aspirational/marketing meme than anything.
“As a nation, we began by declaring that 'all men are created equal.' We now practically read it 'all men are created equal, except negroes.' When the Know-Nothings get control, it will read 'all men are created equal, except negroes, and foreigners, and Catholics.' When it comes to this I should prefer emigrating to some country where they make no pretense of loving liberty – to Russia, for instance, where despotism can be taken pure, and without the base alloy of hypocrisy.” -Lincoln
The fact that it was codified into law in a specific country is an implementation detail. The concepts of liberty in the US documents are philosophical assertions and not related to any nation.
They also happen to be law in the US, but even there they don't really hold force; such "rights" are violated constantly.