That is the original document to certify his birth.
That is the document to certify his naturalization, that’s a different thing. He probably got it when he was 9 or 10.
Does he have any copies of the green card, and what does it say? He should have gotten the green card shortly after arrival, and his parents probably used it to apply for the social security card right away. If those two have the same birth date that he uses now, a good case could be made for the change of the certificate.
If it were me, I’d rather change the citizenship certificate (one piece of paper that’s never used except to apply for the passport), than contact 20 different companies and organizations that have my birth date on file and try to explain them why they should do me a favor by correcting their records.
