The Explanation
When the vet arrived, the first thing she did was to check the state of the puppies. They were healthy and thriving, and Story seemed okay too. The vet assured the couple that there was nothing wrong with the green one and it was just a normal puppy.
Light-colored dogs are born green on rare occasions, likely after contact with biliverdin, a green pigment found in bile while in the womb. The pigment dyes the fur before the puppy is born, and the color fades after the puppy enters the world. The vet assured them that the green puppy would look just like the others in no time. All the twelve puppies were put for adoption later and found loving homes.