I don't think this explanation is very good. We perceive the moon as larger when we see it compared to other objects on the horizon. Out by itself overhead, the moon is a small part of the picture we see. On the horizon, it can look the same size as a building (or trees) off in the distance. But we know the moon is much farther away than the building. Since the building and the moon are about the same size (but we know the moon is farther away), the moon seems much larger than when it is overhead.
(And personally, I don't "think of the moon as being farther away," I know it is.)