Is there any way to explain veridical perception in near death experiences and out of body experiences, naturally? Or is it strong evidence that the mind is a soul?
There is no evidence that "the mind is a soul". This is what's known as the "hard question of consciousness".
There has been some research conducted on "out-of-body" experiences. The only one I can remember offhand was a couple of years ago where words and numbers were placed on top of cabinets in operating theatres. The logic behind this was that if anyone genuinely had an out-of-body experience while under anaesthesia, they would be able to read, and later recall, these words and numbers. I hope I'm not misquoting the findings (I'm doing this from memory), but I seem to recall that they found no evidence whatsoever for these experiences.
It is far more likely that experiences prior to death are hallucinatory and caused by chemical changes, or degradation, of the brain. In a similar way, out of body experiences in an operating theatre are almost certainly the result of similar hallucinations.