Even at that, proper procedure would be (at least now, for a civilian American giving birth overseas) for said civilian to get a US passport for her baby.Was that done at the time????
By the way, I was told after giving birth in Europe, by the American Consulate where I made tracks to get my baby an American BC, that there would never be a record of it anywhere, that that piece of paper was IT for birth certificate for him.
But he does have a passport now so I think he should manage even if it were lost.