Near Death Experiences What (if anything) do they mean?

There have been a number of books recently on the phenomenon on Near Death Experiences (NDEs).  These are reports based on remembered experiences written by people who have physically died for a few minutes and then are brought back to life.  Some people report dramatic experiences of bright lights, heightened consciousness, visions of heaven, a life review, a great sense of peace, visiting with dead loved ones, etc.  These experiences are pretty common with 5% of the population at any given time reporting to have had such experiences.  They also occur in every country and culture studied and seem to have occurred even in the distant past (there are ancient drawings of tunnels and dead people flying up into them.)  The best recent account of such an experience is certainly Eben Alexanders popular book Proof of Heaven (2012).  The book is an exhilarating read and vividly written.

Another recent book is Evidence of the Afterlife: The Science of Near Death Experiences (2011).   I find some interesting  statistical summaries in the second book, but the book is a bit forced in my view.  There is  too much talk about how scientific all of this is.  Also, some of the used methods are not particularly compelling.  For example, while reviewing the stories submitted to the website one of the criteria for determining if the story is fabricated is whether it seems believable to the authors of the study.  
Unsurprisingly almost all the reports make it into the study.  I am not sure that this is a bad thing because having lots of reports is probably a good thing (even if some unknown percentage are invented.)  But there may be some sort of selection bias operating here.

Nevertheless, a few things are pretty clear.  First, it is hard to believe that all of these people are simply lying.  I do believe that a lot of these people (for example, Alexander) are more or less accurately reporting remembered experiences that they had.  So I think it that most of these people are  honest.
There is a lot of overlap among the different stories which suggests that there is a common cause which is giving rise to these experiences (perhaps a fact about human brains perhaps a fact about the beyond.)  But it seems that lots of people (something like millions of people alive today) have had such experiences that were in many respects pretty similar.   Third, the people who have these experiences believe that they are real.  Most have no doubt at all about the reality of their experiences and so the reality of the afterlife.

But are all of these experiences evidence for the existence of an afterlife?  Most philosophers and scientists seem to think no.  The reasoning here goes like this:  All of these experiences seem to (or could) arise from the brain activity.  At the time of death the brain undergoes a pretty dramatic change and this change can cause the brain to fire in certain ways that cause dramatic experiences.  Since these experiences can be traced to the functioning of the brain, they must be illusory.

This type of reasoning is extremely common, but I think that it is deeply flawed. If I were able to track your brain, I would see your brain firing in certain complex ways.  But I cannot infer from this that your experience is an illusion and that the sun does not really exist.  Rather the sun is affecting your brain and your brain is producing the conscious experience.  If all we knew about was the activity of the brain then it would be pretty hard to tell whether there was an external cause or not.  Perhaps the brain activity is caused by some external thing (e.g., the sun) or perhaps it is some kind of an illusion.