From what I've heard about Jane Street interviews from people who interviewed there for intern and new grad positions, they involve solving mathematical puzzles about probability, statistics, and betting. I know multiple people who were invited to onsite interviews, including in one case for a trading position, who were in progress on math and computer science degrees, and had no specific finance knowledge. I also know people who have done trading internships at other firms with no finance experience.

It seems entirely reasonable to me that Jane Street would consider a Bachelor's degree from MIT in math or computer science, being clever, and a prior internship at Jane Street as qualification to work at Jane Street.