the To protect spell and the Armor brooch both stop Magical missile Cold, completely denying the damage. Some creatures (such as tarrasque) have skills that can reflect Magical missile, but Doppelganger do not.
You are dealing with a house rule (possibly including a custom magical item or a property borrowed from another creature) or an error on the part of the DJ (perhaps misinterpreting the Spell Ring).
In character, you could ask, researching to determine the existence of such ability or element.
Out of character, you could ask the DM what it is.