Are you sure? Rule 604 confuse me about that.
The color identity of a card is the color or colors of any mana symbols in that card’s mana cost or rules text, plus any colors defined by its characteristic-defining abilities (see rule 604.3) or color indicator (see rule 204).
604.3. Some static abilities are characteristic-defining abilities. A characteristic-defining ability conveys information about an object’s characteristics that would normally be found elsewhere on that object (such as in its mana cost, type line, or power/toughness box). Characteristic-defining abilities function in all zones. They also function outside the game. #
604.3a A static ability is a characteristic-defining ability if it meets the following criteria: (1) It defines an object’s colors, subtypes, power, or toughness; (2) it is printed on the card it affects, it was granted to the token it affects by the effect that created the token, or it was acquired by the object it affects as the result of a copy effect or text-changing effect; (3) it does not directly affect the characteristics of any other objects; (4) it is not an ability that an object grants to itself; and (5) it does not set the values of such characteristics only if certain conditions are met. #