You are partly right--and I should have clarified this in my previous post.
I'm not denying that the thyroid IS deficient of Iodine in Hashimoto's. It most certainly is. But the first step to addressing this condition is dealing with the autoimmune aspect...not the thyroid. One must be properly systematic in one's approach to this condition or it WILL be made worse.
There are very strong links in the literature between gluten sensitivity and Hashimoto's (so much so, in fact, that the mere elimination of gluten containing grains from the diet can be enough in many cases to bring the TPO antibody count back down to normal). When autoimmune is at issue, food sensitivities MUST be identified and offending foods removed from the diet. The two most common offenders tend to be gluten and casein, but there may also be others.
It is CRITICAL to reduce the TPO antibody count to normal ranges BEFORE embarking on any significant Iodine supplementation. I am in private practice, have delt with this many times before and I have taken a great deal of advanced coursework in functional endocrinology. I know what it is I am talking about.