From my understanding and experience: generally, but not always. I didn't have an interview with Washington, but I did my MA there and the faculty already knew me or knew people who knew me. I've also known people who were admitted to programs without formal interviews, but usually they had arranged to talk informally with a POI prior to or during the application process. I've also been told by people working in admissions that some professors will take students based off prior work and recommendations (usually by close colleagues) alone. So like everything in this process, it's arbitrary and unpredictable.