The dealer where I take my cars to does not use Mazda Moly oil. They usually use Castrol. Most Mazda dealerships seem to have some kind of deal with Castrol, as they usually use Castrol for oil changes. Castrol is also listed in the owner's manual.

As far as a Mazda dealership having to use Mazda moly or Castrol, they're not obligated to. All they need to do is make sure the oil they're putting into the car matches the specifications listed in the owner's manual for that car.