There is a debate on the meaning, but one that has not yet made it's way to the Supreme Court who will ultimately decide. The nuance that you run into is that

There is a debate on the meaning, but one that has not yet made it's way to the Supreme Court who will ultimately decide. The nuance that you run into is that legal opinion defining what 'subject to the jurisdiction of the US' means (from the 14th amendment) was made in 1898, but at that time the border was relatively open. Immigration restrictions started amping up exponentially in the 20th century, especially amidst the world wars. It seems unlikely that the court would have ruled as it did in the context of these new laws.