References are definitely useful. I’m not advocating that people not put references on their resumes, or not call others’ references. But I don’t believe that they are a substitute for a personal statement.
I had a journalism internship one summer, and I was assigned a story about a day school principal who was retiring. I got a lot of great quotes from the students and teachers at his school about what a great principal he was, and about all his accomplishments over the years, and how much they were all going to miss him. I spent some time writing a really thoughtful article and turned it in to my supervisor, who gently let me know that while I had done well with those quotes, I had forgotten the most important thing: to get a statement from the retiring principal himself.