Here is item 5 of the Texas Bar Exam instructions.
5. Proof of Citizenship, USCIS Status, or Other Compliance with Rule II(a)(5): You must provide the documents requested in Question 3.
These documents become part of the Boards file and will not be returned to you. Photocopies of birth certificates will not be accepted.
If you are a United States citizen or a United States national, then you should provide the Board with an original birth certificate issued by a U.S. city, county, or state, or an original Consular Report of Birth. Originals are required.
(If you provided this documentation with a previously filed Declaration of Intention to Study Law, you do not need to provide it again with this Application.)
I have no idea what proof he provided. I assume he has a passport also.