The plant part you are referring to is different. Plants can have toxic fruits or roots or bark or leaves or flowers yet have some other part safe to consume or use. Quantity, season, species, nutrition, and even recent weather events can make the difference between life and death.
In this case, the wood shavings themselves are not what is used as medicine, it's the oil of the nut itself. Black Walnut is use in humans to treat cancer as it's strongly anti-carcinogenic. For a disease that causes tumors to grow along neural pathways, Black Walnut makes sense as a treatment method.
Since it's a strong medicine it would make sense to not use the plant like a safer fodder or bedding plant may be used. Wormwood and Mugwort are potent medicines but if an animal is let to bed in them it can sustain neurological damage or other damage from overexposure.
