From reading the abstract it is not clear if there is really a deficiency. Chronic stress, such as from pain, can cause thyroid hormone levels to rise, which would lock up more of the Iodine in the system. This is not really a deficiency, but rather a mobilization of the iodine.
In the second article there is a statement that the thyroid regulates adrenal function. Actually it goes both ways as they have a feedback mechanism with each other. For example the conversion of T4 to T3 requires sufficient cortisol levels being secreted from the adrenals.