Here's the short of it: You can use gelatin to filter cruddy used deep-frying oil until it is crystal clear. The technique is easier than any other method I know, requiring no wire strainers or coffee filters or extensive clean-up.
When this guy* made clear ketchup, he used egg whites to separate remaining solid tomato matter out from the liquid tomato umami. Wonder if that would work for oil at all.
Both methods just use protein to trap large particles. The difference is that with gelatin, the process is reversible with heat. Magnesium silicate is just really pure talcum powder and it's widely used in food service to clean oil.