I would think their state of sleep is different than ours. Fish do not sleep, they sort of hang out at the bottom of the tank. I notice that Omar will often sleep in a vertical position holding on tightly to his vine. If they would have the same sleep state I would think they would not be able to hold on the branches (vertically or horizontally). Mammals at different points in sleep are "paralyzed" during dream states, I think. So we are totally relaxed and could not maintain a position like the chams.
It suggests to me that because of their primitive brain structure they do not need to have such a sleep state. Additionally, I think it is also an survival thing so as a prey animal they may be able to awaken more quickly and escape the predator.