Alright, here's a real Crackpot Theory: Nanaki is also insane.
Nanaki "knew" Kanade would get kicked out eventually, which must mean either a) Nanaki knew Kanade hanging out with her would get her kicked out, or b) Nanaki was able to tell that Kanade was "different" from her group (she is insane), which would cause a rift. If Nanaki could tell that Kanade was insane, yet keep up the facade that "she's a nice girl", she's insane. If Nanaki knew her hanging out with Kanade would get her friends to leave her, she was trying to isolate her, so she's insane.