I'm thinking -- if you speak with an accent you can get away with being a "foreign student," but if you sound more or less like an American, odds are people won't take you for a foreigner. She must have been a very loopy old dame to introduce her Hawaiian-born protege to people as a foreign student, and not notice their reaction and adapt her thinking.
“I was taken aback by how enthusiastic she was about him,” Hulton says. “And I believe she said he was from either Kenya or Indonesia, and I favor Indonesia in my recollection.”
This is the suspicious part. If you hear "Indonesia" and "Kenya" over and over again for the last five years of course you're likely to think she said "Indonesia" or "Kenya," but for all we know she could well have said "Togo" or "Guinea-Bissau" or "Sierra Leone."
"Kenya or Indonesia" is a pretty strange combination, rather than "Kenya or Tanzania" or "Indonesia or Malaysia". It's hard to see how that could have been what he actually took away from the meeting at the time, rather than something he "remembered" because of all the hoopla about Obama years later.
He probably was a foreign student. Had various IDs, used whichever one suited.