I think the point of the story was that Cutie could follow orders and prevent harm properly without conscious knowledge of its doing so. Though it consciously believes the humans are going to dissolve themselves, its unconscious circuitry knows otherwise. Does that make sense? Or maybe it's just a plot hole. But I think the purpose of the story is to point out that Cutie can follow all the laws of robotics without realizing it.
Could work. On the other hand, Asimov later described a situation where the protagonist suspects someone of conspiring to have robots unwittingly kill lots of humans, by shooting as space ships (which the robot would believe are just other robots).
More generally, I never spot a story where robots have unconscious cognitive processes. It seems everything they do is deliberate, even though the humans around them don't fully understand what is thinking on.
