Turning a cloned creature face-down does not remove its abilities

What I expected:
A permanent has copied another creature via a clone effect. Turning it face-down should remove its abilities and turn it into a plain 2/2 creature.

What I observed:
It becomes a 2/2 face-down creature, but retains its abilities.

To reproduce:
Play an Ulamog, the Infinite Gyre. Play Sakashima, the Imposter copying Ulamog. Play an Ixidron. Ulamog and Sakashima are turned face-down and become 2/2, but Sakashima still has indestructible and annihilator 4.

The relevant rules text:
707.2 Face-down spells and face-down permanents have no characteristics other than those listed by the ability or rules that allowed the spell or permanent to be face down. Any listed characteristics are the copiable values of that object’s characteristics. (See rule 613, “Interaction of Continuous Effects,” and rule 706, “Copying Objects.”)

707.2a If a face-up permanent is turned face down by a spell or ability, it becomes a 2/2 face-down creature with no text, no name, no subtypes, and no mana cost. A permanent that enters the battlefield face down that wasn’t cast as a face-down spell also has these characteristics. These values are the copiable values of that object’s characteristics.