Therefore, wouldn't it be theoretically possible to have a similar bypass mechanism in a thyroid with an insufficient or poorly functioning peroxidase? That would explain my differential response based on the form of iodine supplementation.
But does such a bypass mechanism exist?
I can't find any evidence for the claims of the author that you quote. As far as I am aware, there is no evidence for uptake and concentration of iodine by the non-lactating breast.
There are some very old
studies showing that both iodide and iodine treatment of women with fibrocystic breast disease led to significant and similar levels of improvement in the disease. The two forms weren't compared directly but in separate studies. Molecular iodine was preferred because of fewer side effects.
This series by Ghent seems to form the basis of all the claims about the role of iodine in the breast, but it doesn't really tell us very much - just that iodine/iodide treatment helps fibrocystic breasts.
It might have nothing to do with the direct action of iodine on the breast, in fact,
this study shows that oral administration of molecular iodine does not result in the appearance of molecular iodine in the blood. Rather, some is converted to iodide while the bulk reacts with lipids and proteins before or during absorption and circulates in this form.
I have never seen any detailed follow-up studies of the fate of this iodinated protein and lipid and what biological role it might play, but it puts paid to the notion that breast cells somehow take up and respond to molecular iodine. It could well be that these iodinated species have some biological effect and this could be the basis of the different apparent action of molecular iodine and iodide but no-one seems to be studying it anymore.
Another
study showed that molecular iodine in the gut reacted with deiodinated T4 metabolites to reform T4, leading to increased T4 in the blood.
These studies were in rats and the situation may be different in humans. What they do show, however, it that the fate of oral doses of molecular iodine is complex and doesn't fit with the simplistic assumptions made by the proponents of the special role for iodine.
I don't discount that there could be a role, it's just that there is no good evidence to even hint what it is.