Dude, or Dudette,
You may wish to understand what an iodine number is, before making wrongful conclusions that merely because a substance may have an iodine number associated with it, does not mean that it contains iodine.
Iodine number is a test for unsaturation present in hydrocarbyl chains of materials. The olefin bond reacts with iodine, absorbing it. Many wet analytical chemical methods seeking to determine unsaturation in an organic sample will treat a known amount of substance with an excess of iodine, and then back-titrate the excess iodine using a thiosulfate solution. The difference between the initial added amount of iodine, often in the form of WIJS solution, and what is accounted for by the thiosulfate is reflective of the unsaturation present in the material being tested.
All chemists of reasonable skill recognize that walnut oil, and all plant-derived oils, contain unsaturation. Hence, iodine number is a common test.
The article you cited is interesting, but I find no evidence that walnut oil contains iodine in it anywhere in the article. If you point out specific passages in there that you base your belief on, I'd be happy to have another look.
Simpleton info on iodine number here:
If you would like a reference to an ASTM test method, just ask.
Walnut oil has NO iodine.