Ekim,
I have no problem with anything you say here. The point I take away from it is that she emphasises that there is no need for any of the trappings of religion etc. to be able to have a much greater empathy and compassion towards others after such an experience, that you can have spiritual experiences which do not have to relate to some sort of supernatural ideas, just as one can achieve the same by a host of other experiences, especially when one has been close to death or by meditation techniques, as you say. I think it is quite appropriate, using her words, to call it as being a 'secular spirituality' based upon 'a scientific inquiring understanding of what it means to be human'.