I'm not sure what you mean by "organic" iodine. Iodine is an inorganic element. It will be inorganic no matter where it exists; because it is a simple element. Do you mean that it is better to ingest Iodine while it is assimilated in seaweed; instead of when it is recovered from seaweed?
As your article indicates, the only other sources are where it is found with other inorganic materials; such as in Chilean saltpetre, caliche, old salt brines, and salt wells.