It was actually worse than tribdog described. A mother and daughter were struck by lightning. The mother was killed and the daughter knocked unconscious. Nearby was some sort of eland sort of animal. Since it was just sort of standing there, some of the men speared it. Just as it dies the little girl came to. One idiot, the first shaman, apparently, decided that the life that had left the animal had gone into the girl and restored her. He skinned the animal and laid the skin on the mother, hoping to restore her as well, but it didn't work. Still though, the practise of trying to control the forces of nature through magic had begun.
The main trouble was that instead of saying "Here's the sort of coincidence that might have given people the idea of spirits/magic, they just presented the whole thing as if it'd been recorded as fact on a stone carving, or something.
They asserted without qualification that the Neanderthals had lost to the Cro-Magnons in competition for food and shelter, and had thus died out, when that is just one train of speculation on the matter. It's pretty absurd to say we know anything about Neanderthals. They've only found the remains of 80 individuals and those span something like 130,000 years.