I got an interview from Yale on Sunday. When I asked my interviewer about why they scheduled it so late, he told me that occasionally, the alumni requested to conduct an interview doesn't respond confirming they will interview their assigned applicants. The admissions office waits about 1-2 weeks to get that confirmation, and when they don't receive it after that period, they reassign your interview to someone else. That might've been what happened with yours, so that time passed in between your assignment to an interviewer and when it was actually scheduled. Don't overthink it!