Edit: I've looked into this and am updating it to the full answer. Here goes...
Re. Habermas and his claims in particular
I emailed the source of these claims, Dr. Habermas, to try and obtain the "list of over one-hundred evidential cases" he refers to in his debates/talks. He did not have such a list (I can provide the exact email if requested). He suggested checking out his book, Beyond Death and other articles/interviews/etc. for more sources.
I followed up with a request for a reference to the girl who was underwater for 19 minutes (mentioned in the question, with a video link). He provided a reference to the journal in which the article appeared, the journal, Current Problems in Pediatrics and Adolescent Heath Care.
I tracked down the article, available from Dr. Morse's (the author) SITE, available for download HERE. The mention of that case is, indeed, very short and disappointing, which surprised me if Habermas' account of the same girl is correct; compare the amazing story in my question by Habermas with Morse's account here:
I reported the first pediatric NDE, a 7-year-old girl who was without spontaneous heartbeat for 19 minutes and had fixed and dilated pupils. She recovered to give a detailed description of her own resuscitation including hearing pieces of conversations in the emergency room, accurately describing her own resuscitation with details such as nasal intubation and being placed in a CT scanner. This was followed by a spiritual journey with a spirit guide through a dark tunnel to a heavenly realm and a decision to return to consciousness.
No mention of seeing her mother/brothers at their home some distance away and recalling details which were all verified to be true. The fact that she recounted details about what was happening to her own body are far less impressive, at least to me. The paper cited for this short summary is HERE and I don't have access, so I admit the possibility that far more details are present in the original paper.
I will note that Morse's site (linked above) is absolutely filled with references to religion (Jesus/Christianity in particular), a spirit/soul, etc. While these details don't establish anything by themselves, I'm simply noting that he may have a particular interest in these experiences leaning in one particular direction.
Lastly, I'll note that Morse believes he can successfully remote view. The religious motivations are one thing, but belief in remote viewing abilities are another.
- HERE Morse presents a document showing how he successfully remote viewed (cough)
- HERE, Morse performs a remote viewing live on video. I noted that his adjective list includes about everything one can imagine in describing what he's "seeing," many of them seeming like antonyms: lights, darks, flat, etched...
Near Death Experiences in general
To close up, I'll list some interesting material I found on NDEs in general.
- THIS is an absolutely outstanding summary (fairly up to date as well) of NDE studies by Keith Augustine, including specific cases, references, and all. Just wonderful. Notable statements include:
- HERE is a section showing that non-Western NDEs have almost none of the features of "prototypical Western NDEs," decreasing the probability that an NDE is a snapshot into an objective, universal post-death reality by the NDEr
- HERE, Augustine presents essentially what I was looking for in a section called, "Veridical Paranormal Perception During OBEs?" He takes several cases and shows that there need be nothing "paranormal" about patients' recollection of details. He also states that no conclusive studies have cleared the air about whether any details have been 1) impossible to know without "leaving" the body and 2) verified conclusively:
But at the end of the day, we are left with no compelling evidence that NDErs have actually been able to obtain information from remote locations, and we have clear evidence that NDErs sometimes have false perceptions of the physical world during their experiences.
- THIS paper examines near death experiences in cardiac arrest patients and makes this statement:
It is not clear whether the experiences of patients, who report that they have ‘left their bodies’ and viewed their own resuscitation procedures are veridical or are hallucinations. Some patients do appear to have obtained information which they could not have obtained during unconsciousness. If this is so, it would suggest that some element of human consciousness is capable of separating from the body and obtaining information at a distance. However, it is also possible that the information that they report may have been gained from ordinary sensory sources. In this study, no out of body experiences occurred. The authors know of no prospective studies which have helped clarify this point.
- Not necessarily related, but THIS study shows that Catholics, Muslims, and atheists experience NDEs at approximately the same rate of occurrence (NDEs per survived cardiac arrest patient).
So, it seems that at least two investigators familiar with the area of inquiry (Augustine's full article displaying an extremely long list of sources) have concluded that at least no known experiment has confirmed that a near death experience allowed a patient to see details that were later verified to be true and could not be learned by any method other than leaving the body.
As an entertaining piece of dessert, I recalled James Randi's own Out of Body Experience, found HERE. He "floated" out of his body one night and recounted vivid details to his step-son the next morning (color of bed spread, where his cat was on the bed, and what the cat's eyes looked like), only to find that the specific bedspread was in the laundry and that the cat had been outside all night. Not an NDE, but in listening to him, it sounds like such a "typical" OBE, and it's just so fantastic that Randi of all people experienced it and then learned it was not real.