Why do garbage disposal companies suggest using cold water with their products?
Assuming that food waste disposers will include more grease going down the drain due to the variety of items being disposed, I've been told that cold water helps coagulate grease into chunks that wash down the drain. Somehow this helps reduce grease buildup in the trap. I would suspect that cold+liquid grease at the disposal gets broken up without gumming up the works, but warm liquid grease will coagulate in the cutters/trap as it cools and settles.
According to this GE Disposal User Guide (PDF)
Do not use hot water while running the disposer. Cold water will keep food waste and fats solid so they can be flushed down the drain.