The name Barry Soetoro being on the BC is unlikely and not the problem. Why would Skanky Mama and LoLo ammend his Hawaiian records from half-way around the world when there was no indication they’d ever return to live in Hawaii? They wouldn’t. A LEGAL adoption by LoLo is questionable for that matter. More likely they just said Barry was adopted and he began using the Soetoro name instead of Dunham the same way it was often done a century ago in the US.
Daddy’s Name on the BC is the problem. My guess is that there isn’t a Daddy’s Name on his BC other than UNKNOWN. How do you prove UNKNOWN is a US citizen?
It all comes down to Who’s Your Daddy? More than 70% of blacks today don’t know. Occam’s Razor.
It depends on whether you accept that it is possible one or both was involved with the Spooks.
Even if you don’t accept they were spooks -
Was it done to help him gain permanent resident status in the US? IIRC, he was eventually granted permanent status.
In his immigration file they talk about Barry and his relationship to Lolo.
In 1967 it is noted that Barry is considered a step son.
Btw, there was indication that Lolo wanted to come back to the US in those files.