Black walnut hull tincture...iodine! EUREKA

Perhaps you are thinking of a different nut. Black walunts come in a tough green outer hull covering. One cannot simply pick them off the ground and throw them at a wall. They would need the tough 1/2" thick green hull removed first. This Black-Walnut hull coating is well-known for its anti-parasitic qualities. Presumably you left the step out of how you removed the hulls, or perhaps you were picking up something else.

Also, given that the soils in the midwest are well-known to be depleted in iodine, I have doubts about any nuts containing enough Iodine to cause a stain. At the level of concentration required, the inside would be effectively sterile. So, if the purported Iodine doesn't come from the soil, then wherefrom cometh it ?

It is well-known that tannins and other polyphenolic compounds, gallates, catechols, etc. are what give rise to color in nuts. A single mature Black-Walnut tree can be worth $ 20,000 in lumber, there aren't many of those around.