I don't know anything about organic garden ducks, but organic ducks themselves haven't been treated with any chemicals. They aren't fed any hormones or antibiotics and are raised as free range so the poultry doesn't undergo unnecessary stress. I'm guessing organic garden ducks are organic ducks raised in a garden-like setting...?
Organic anything is items or animals that have not been treated with chemicals. I would imagine an organic duck has been raised in captivity and not fed any chemicals or hormones.
An organic duck is a duck, raised in captivity, like on an orchard, just to be eaten. Some people raise ducks, just to eat them, like chickens. My friend actually has some 'organic ducks' that he raises and eats.
Organic ducks are not fed anything that has been grown or treated with a chemical. Most likely he means that this duck was fed things out of his organic garden.