Earlier quoted context omitted.
But don't you have to renounce all other allegiances? Uruguayan law says that even if you renounce your uruguayan citizenship, you still keep it. I think this was put in place exactly because lots of Uruguayans were leaving for the USA (lots of Uruguayans is something like 50).
No, the USA does not require that.
But it doesn't mean that you actually renounce citizenship of your home country.