That isn't a contradiction, not all fatty animal byproducts are edible, or at least not without filtering, sterilization, or other steps defenders may not have had available.
Also, animal fat for such uses can be made out of any meat. Rats, dogs, diseased animals, horses, and in principle even human corpses.
Not to forget using the stuff that is beyond acceptance by everyone. Animal fats can keep, but there is always some limit. At point it is so rancid that no one wants it. Either you burn or dump it.