But maybe they DID think it through, when they put in "subject to the jurisdiction of". That would be the clarification point. Meaning, a baby born to foreigner parents would not be subject to the jurisdiction of the US, but of the country to which their parents belonged to.
if a foreign diplomat was not subject to the jurisdiction of the US, then why would a person here illegally? Either you are saying that a diplomat is not subject to our laws, meaning they could break them with impunity, or, "subject to the laws" was not what they meant.