But, if he was an Indonesian citizen and used that citizenship as a teen and young adult, could he reclaim his American citizenship without being naturalized? These are important issues that need to be resolved.
If Obama was an American citizen by birth (e.g., if he was born in Hawaii), he would not lose his American citizenship even if he later took on another country's citizenship, according to the Supreme Court's decision in Afroyim v. Rusk.
I don't think he had any American Citizenship to be regained. But you can speculate that he had some filings in August of 1961 that supported an argument that he did; then came back from Indonesia at an appropriate time and got the paperwork effectively affirming a recapture of the citizenship (which he may have never had); then used the documentation he got in the recapture proceeding to get passports and other evidence of citizenship.