At the time all schools in Indonesia were controlled by the Government and only Indonesian citizens WITH THE PROPER PAPERS could go to them. Indonesia at the time was a dictatorship and lil Barack Obama could not attend those schools unless he was an Indonesian citizen and he had been adopted legally in Indonesia.
He was adopted at five or before he turned five by Lolo Soetoro and his mother gave up all legal rights to him because under Indonesia law only Muslim Fathers had right to their children.
Interestingly enough there is a methodf of reaffirming your US citizenship at the age of eighteen in cases like these of dual citizenship where one country Indonesia doesn't recognize dual citizenship with other countries like the United States. If Barack Obama didn't reaffirm his US citizenship at eighteen it could be tantamount to losing it.
CHAPTER 3-LOSS OF NATIONALITY349 LOSS OF NATIONALITY BY NATIVE-BORN OR NATURALIZED CITIZEN
SEC. 349. [8 U.S.C. 1481]
(a) A person who is a national of the United States whether by birth or naturalization, shall lose his nationality by voluntarily performing any of the following acts with the intention of relinquishing United States nationality-
(1) obtaining naturalization in a foreign state upon his own application or upon an application filed by a duly authorized agent, after having attained the age of eighteen years; or
(2) taking an oath or making an affirmation or other formal declaration of allegiance to a foreign state or a political subdivision thereof, after having attained the age of eighteen years; or
(3) entering, or serving in, the armed forces of a foreign state if
(A) such armed forces are engaged in hostilities against the United States, or
(B) such persons serve as a commissioned or non-commissioned officer; or
(4)(A) accepting, serving in, or performing the duties of any office, post, or employment under the government of a foreign state or a political subdivision thereof, after attaining the age of eighteen years if he has or acquires the nationality of such foreign state; or
(B) accepting, serving in, or performing the duties of any office, post, or employment under the government of a foreign state or a political subdivision thereof, after attaining the age of eighteen years for which office, post, or employment an oath, affirmation, or declaration of allegiance is required; or
(5) making a formal renunciation of nationality before a diplomatic or consular officer of the United States in a foreign state, in such form as may be prescribed by the Secretary of State; or
(6) making in the United States a formal written renunciation of nationality in such form as may be prescribed by, and before such officer as may be designated by, the Attorney General, whenever the United States shall be in a state of war and the Attorney General shall approve such renunciation as not contrary to the interests of national defense; or
(7) committing any act of treason against, or attempting by force to overthrow, or bearing arms against, the United States, violating or conspiring to violate any of the provisions of section 2383 of title 18, United States Code, or willfully performing any act in violation of section 2385 of title 18, United States Code, or violating section 2384 of said title by engaging in a conspiracy to overthrow, put down, or to destroy by force the Government of the United States, or to levy war against them, if and when he is convicted thereof by a court martial or by a court of competent jurisdiction.
(b) Whenever the loss of United States nationality is put in issue in any action or proceeding commenced on or after the enactment of this subsection under, or by virtue of, the provisions of this or any other Act, the burden shall be upon the person or party claiming that such loss occurred, to establish such claim by a preponderance of the evidence. Any person who commits or performs, or who has committed or performed, any act of expatriation under the provisions of this or any other Act shall be presumed to have done so voluntarily, but such presumption may be rebutted upon a showing, by a preponderance of the evidence, that the act or acts committed or performed were not done voluntarily.
[SEC. 350 was repealed]
351 RESTRICTIONS ON LOSS OF NATIONALITY
SEC. 351. [8 U.S.C. 1483]
(a) Except as provided in paragraphs (6) and (7) of section 349(a) of this title, no national of the United States can lose United States nationality under this Act while within the United States or any of its outlying possessions, but loss of nationality shall result from the performance within the United States or any of its outlying possessions of any of the acts or the fulfillment of any of the conditions specified in this chapter if and when the national thereafter takes up a residence outside the United States and its outlying possessions.
(b) A national who within six months after attaining the age of eighteen years asserts his claim to United States nationality, in such manner as the Secretary of State shall by regulation prescribe, shall not be deemed to have lost United States nationality by the commission, prior to his eighteenth birthday, of any of the acts specified in paragraphs (3) and (5) of section 349(a) of this title.
Key phrase. You have to prove that he or his mother intended to relinquish his US nationality and citizenship. No proof of intent, no loss of citizenship.
It goes the other way. In order to lose his natural born citizenship, he would have had to renounce it after the age of eighteen. What his parents may have done doesn't matter. Nor does Indonesian law.