Home births were not all that unusual among the hippy crowd.
If his mama or grandma would have done home-birth paperwork he would not be hiding the COLB.
If they had faked a home birth to assert US citizenship for an actual foreign birth within 5-7 days of the actual DOB they would have likely pulled it off. Apparently, that is not what happened.
That thought never came to my mind. What if .... ? I don’t know what the outcome would be.