So, it's possible the family just went there to have the baby born there? Like a reverse US immigrant anchor?
When my ex was playing football in Canada, my daughter was born. We had been there 6 months prior. She was 3 weeks old when we came back to the states. Talk about a chore! We finally got her admitted into the states, but had to send our birth certificates, our marriage license, and her Canadian birth certificate back to the border crossing to make it legal.