I will respond more in depth later, but I am HIGHLY familiar with "out of body" (OBE) phenomena. These experiences are very common and can even be self-induced. In fact, they frequently are by those who practice or engage in the magickal arts, meditation, hypnotism or anything else which allows for a state of deep trance. Some individuals are even able to do this naturally, usually from young childhood, without any form of training. Only later do they realize they are different from most others. In the vast majority of cases, this experience occurs during the theta stage of trance/sleep. It can also occur during times of profound physical stress, such as serious injury or illness (more on that later).
An OBE experience occurs when the astral body, complete with a carbon copy of one's own consciousness, separates from the physical body. This separation of the astral body from the physical body is normally referred to as an astral projection. During astral projection one's astral body and consciousness reside within the astral realm, rather than the physical realm, allowing one to experience this alternate dimension with their astral senses.
This is what occurs during near death experiences. As stated above, this is something that, with training, can be induced at will. One's degree of proficiency will depend on a combination of natural ability and training/practice.
To most people this sounds like something out of a fairy-tale, or simply a bunch of hogwash. Intellect is not a deciding factor here. Many intelligent people are completely unaware of the vast spiritual realm which exists all around them and which influences every aspect of their lives. On the other hand, vast networks of people all over the world are not only aware of this reality, but they enter the astral realm with regularity (for either good or bad). It is rarely discussed, at least on a personal level, with those who deny the existence of anything outside of the physical. This is especially true when dealing with those who consider themselves intellectuals, as their arrogance often prevents them from being able to acknowledge that large numbers of less educated people know something they don't. This is especially true when addressing subjects of such magnitude. In most cases the conversation ends with the uniformed scoffing in disbelief and the knowledgeable quietly chuckling.
Therefore, these kind of discussions are rarely productive, but they are possible if both parties are respectful.