Thank you for posting that copy of the record. I no longer had it.
I disagree , this was made public as you said in 2007, no reason at that time for funny business. Why would Lolo risk being busted for lying? It was a law you must be a citizen of Indonesia to attend the schools that he did. Why wouldn't Lolo adopt him? I think it is a very reasonable expectation that he did. Take a child away from the US back then and not adopt? Pretty risky, I think for many reasons that Lolo would not adopt him. His sister Maya is Lolo’s. I think bo would have complained about his sister having a different name. Back then adoption was far more common, if not almost expected.
Since there are no records at all of Lolo adopting Barack, I assume that it was a “casual” and not legal adoption. Most stepparents do this. Plenty of times the child takes the last name just to be the same as the rest of the family, but no adoption legally takes place.
Of course they would have told the school in Indonesia that Lolo was his father or adoptive father so he could attend. This doesn’t mean it was legal. My oldest attended private school under his not-legal stepfather’s last name.