I found this interesting article showing that not only a selenium deficiency, but an iron deficiency and/or toxic chemicals have to be there in order for Hashi's to appear along side iodine supplementation.
Autoimmune thyroiditis, a.k.a, Hashimoto’s thyroidits, is characterized by infiltration of the thyroid gland by inflammatory cells and production of autoantibodies to thyroid-specific antigens, thyroglobulin and thyroperoxidase. Autoimmune thyroiditis accompanies and is considered a main cause of hypothyroidisim since it results in destruction and eventual fibrous replacement of thyroid follicle cells.57
Although excess iodine intake has been singled out as the cause of autoimmune thyroiditis, current research clearly shows that this condition is multifactorial in etiology. Deficiencies of other key nutrients, genetic susceptibility, and exposure to environmental pollutants are all contributing factors. Iodine repletion without at least one of these other factors, is insufficient to cause autoimmune thyroiditis.
It is well recognized that increased iodine intake results in increased iodination of thyroglobulin, which, since this process also results in increased production of H202, increases thyroglobulin’s antigenic potential. In addition, since H2O2 is one of the compounds known to stimulate the intracellular adhesion molecule-1 (ICAM-1) promoter to increase transcription of the ICAM-1 gene, increased iodine intake (which can result in increased levels of unquenched H2O2) can also upregulate expression of ICAM-1. Iodine therefore has significant potential for harm; however, for this potential to be actualized, at least one or more of a number of other contributing factors must be present. These include selenium deficiency, iron deficiency, and/or exposure to environmental pollutants.58
58. Zimmermann MB, Köhrle J. The impact of iron and selenium deficiencies on iodine and thyroid metabolism: biochemistry and relevance to public health. Thyroid. 2002 Oct;12(10):867-78.