Considering Obama seemed to think he could fabricate his background freely, as evidenced by his submission for his autobiography, it is not unreasonable to believe he would lay claim to being a foreign exchange student for the benefits it provides.
People like Obama see nothing wrong with lying if you are cheating the corrupt system he hates.
Or he may have claimed foreign student status because he had foreign nationality. Or he was using a different name. Or he wasn’t there, or at least not there during the same time frame claimed. There are many possibilities. Of course the names of classes he took (if he was there and took any) would likely be very interesting, and grades.