A proper electric fence controller will deliver a short, high voltage spike about once per second -- plenty of time to disengage. The concept of the electric fence is to discourage animals, not electrocute them.
This, apparently, was not a “proper” electric fence. And there was ground water involved. This was a widely reported (in that part of Alabama) incident at the time and my mother also remembers the story. Can I swear it happened? No. But I believe it did.