I think the story of Lazarus and the Rich man holds a key biblical insight on this topic.
"And he called out, ‘Father Abraham, have mercy on me, and send Lazarus to dip the end of his finger in water and cool my tongue, for I am in anguish in this flame.’ But Abraham said, ‘Child, remember that you in your lifetime received your good things, and Lazarus in like manner bad things; but now he is comforted here, and you are in anguish. And besides all this, between us and you a great chasm has been fixed, in order that those who would pass from here to you may not be able, and none may cross from there to us.’" —Luke 16:24-26 ESV
Jesus is pretty clear in pointing out that those who "pass from here" are not able to come back over once they have died. I don't see any way around our Lord's words. So, I think you are correct with your assessment that such stories are explained physiologically and/or psychologically. Since the soul may not "cross over" once it is in heaven, or hell, then that must mean this man didn't really die and we must find another explanation for his experience.
Thanks, Jim! Good stuff!