Producer Hamasaki

Does Ayu produce her own music? All her CDs say that she's produced my Max Matsuura, but he says she produces her own music and her CDs say "Produced by Max Matsuura" because of the contract she signed. Is this true?

And if you don't know what a music producer does:
record producer (or music producer) has many roles, among them controlling the recording sessions, coaching and guiding the performers, and supervising the recording, mixing and mastering processes.