The part of Indonesian law that provides that a child under five adopted by an Indonesian father is an Indonesian citizen is automatic. Unlike other provisions, it does not require that the child take any action to renounce some other citizenship.
You are right that little Barry’s status under the Indonesian statutes did not terminate his US citizenship. It is not easy for a minor to affirmatively renounce US citizenship. And he was not required to do so under that Indonesian provision.
However, US law at the time Barack was in college provided that if an ADULT takes certain actions respect to establishing citizenship in another country (for example, obtaining a passport), then he loses US citizenship.
Did Barack, after turning 18, make an affirmative application to renew his Indonesian passport? That would appear sufficient under US law to cause him AT THAT TIME to lose his US citizenship, without the US state department necessarily even knowing about it.
IIRC the Haugue agreement did not allow for joint citizenship if one country was not in agreement. At the time BO was in Indonesia, their regime did not allow joint/dual citizenship.
For what it’s worth, Sir John, this has been my gut feeling all along: That regardless of where he was born, the real clincher is that as an adult he might have tried to use Indonesian citizenship as a door-opener for obtaining benefits of some kind, most likely at Columbia University. Your avenue of investigation most surely needs further exploration.
That assumes he was adopted and had Indonesian citizenship to begin with.