No, that's a very unlikely scenario.
While it is certainly possible that an admissions office could be, depending on the university, quite delighted to readily admit foreign students, it is much more likely the reason is quite cynical: Foreign students virtually always pay full out-of-state tuition. Foreign students in the early 1980s had no access to standard federal loan and grant programs.
Also, Obama claims to have lots of student loans. He wouldn't have been eligible for federal ones if he was coming in as a foreign student. Indeed, I would be surprised if the state of New York or Columbia offered any type of support for foreign students other than the standard graduate-type assistance, such as teaching assistantships. Since Obama was an undergraduate, it would be unusual for him to receive any graduate support and there is certainly no indication that he did.
In short, there is no academic advantage for Obama to have claimed foreign status, and there is a distinct economic disadvantage.
Totally agree.
He may have entered college as an Indonesian. He had the passport and was an Indonesian citizen. Indonesia may have provided him some scholarship money for all we know.
There isn’t assistance from the USA or the institution itsel for foreign students. But there often is money from their own country to sponsor their learning in America.