I think there is certainly a lot of truth in this statement, however, I would argue that fear is less of a conspicuous element in this short story than it is in other short stories such as "The Pit and the Pendulum" or "The Tell-Tale Heart." This is because more focus is placed on the narrator's anger and violence thanks to his drunkenness rather than the emotion of fear. Fear, when it does spring up, only occurs after the narrator has killed his beloved black cat, Pluto, and then has been shocked to find that another, seemingly identical, black cat has taken its place. The way in which this black cat bears a white mark wear the original Pluto was hung and his affection towards the narrator fills him with a terrifying fear:
Alas! neither by day nor by night knew I the blessing of Rest any more! During the former the creature left me no moment alone' and, in teh latter, I started, hourly, from dreams of unutterable fear, to find the hot breath of the thing upon my face, and its vast weight--an incarnate Night-Mare that I had no power to shake off--incumbent eternally upon my heart!
Clearly, we can see therfore that fear is a definite factor in this story, but it is not a "natural state of being." It is only created by the actions of the narrator, and is equally balanced by the "evil thoughs" that become the narrator's "soul inmates" thanks to the fear and stress he is under.