"I suppose it might be likened to someone without any appreciation or knowledge of opera, being confronted for the first time by Der Ring des Nibelungun, and a lover of Wagner being requested to explain what it meant to them."
And this, it seems to me, is the real issue. Someone uneducated or interested in religion, faced with a some sort of spiritual experience - An appreciation of a cathedral architecture, for instance, or a painting inspired by a religious event, or a majestic piece of religious music may not get the academic points or references but still be effected by the piece itself - and,given that we are talking about a spiritual/emotional response, how can you quantitatively measure this response?
Seems to me that this notion that theists experience a spiritual component that non-theists do not is purely an assumption of the theists, without any supporting evidence...