I would assume they just dump a few handfuls of ice in the disposal and turn it on with water running over it. When the beaters break the ice it will form sharp edges for a short period of time that remove any material buildup inside the disposal.
It's less the sharpness than the solidity. An integral mass hitting clog or debris will scour those off regardless of how sharp the edges are. It's a bit like the principle noted in the meterological sector regarding hurricanes wind speeds: it's not that the wind blows, it's what the wind blows.
Ice is good for cleaning garbage disposals. Citrus peels (lemon especially) is good at improving their odour.
