No one said it was magic. You make ice cream within a fairly narrow range of temperatures because you want it cold enough to be ice cream but not so cold as to be ice cream that you need a hammer and pick to eat. Ice-cream machines are designed to provide this temperature. As you noted, if you replaced the sugar for salt, you'd have double the depression effect, thus keeping it from freezing within the temperatures used to make ice cream. That's not to say it'd never, ever freeze. It just probably wouldn't freeze in your ice cream machine.
It's entirely possible that there was just a very minimal amount of salt used because perhaps they didn't sweeten their ice cream with sugar much; I guess you can also use condensed milk for sweetness. But if there wasn't enough salt to make it unpalatable, that negates the whole "And he ate the WHOLE thing!" aspect of the story.
Edit: This is also a sterling example of the sort of dumb shit we're willing to argue on this forum
Edited, Sep 29th 2012 1:57pm by Jophiel