After some thought, I see a practical reason for someone to insure he had proof of citizenship namely child custody jurisdiction.
The normal laws of states at that time is that a child born in wedlock would be a citizen of the state where the father is a citizen. An exception would be if the child was born out of wedlock and then it would be the mom’s state.
If there was a concern that custody issues would arise, the mom would be much better off if the child was a US citizen rather than an immigrant (think Cuba and Elian).
So I take back my original granting of your premise and disagree with your reasoning. However, the exercise is still irrelevant for me because I think the weight of the evidence is that he was born in Hawaii.
Your fingers are faster than mine - I was thinking the same thing!