The way I understand this with my very basic chemistry knowledge, is that most substances are either water soluble, or fat soluble. If they're water soluble, it's generally easier for our bodies to get rid of them. When they are fat soluble, they tend to stick around more, and it's generally accepted in the mainstream medical community, that fat soluble toxins tend to accumulate in fatty tissues.
AV's idea regarding combining starch with fats to remove toxins, was that they would combine to form a kind of internal soap, for loosening and safely carrying away toxins.