So, to me, for someone to say that they are “spiritual, but not religious,” means that they are saying something to the effect of “I’m a human being.” 

Of course, I’m being deliberately obtuse with my own question, because what people generally want to convey with that statement is that they simply do not subscribe to any form of organized religion, and prefer to find their own method of making sense of the world; that they do not find any meaning in the structures others have created, but prefer to create their own order within the chaos.