he could have received private financial aid such as from Indonesia or a private individual or scholarship. also if he had green card or refugee or parolee status he might have been eligible for aid from NY state.
If Obama really was a citizen of Indonesia then where the HESC was concerned he would have been better off lying and saying he was a citizen of the U.S. HESC is a state agency for state residents. Its rules say that their grants and scholarships are for U.S. Citizen residents of New York state only. To qualify as a resident you need to have lived in the state for at least 12 months prior to the first semester in college, or have completed your last two semesters in an New York high school. For Obama, or anyone else, to apply as a foreign national would be useless so far as that organization is concerned. It would have gained him nothing.