Vitamin A for one is needed for the Iodine uptake by the thyroid.
So if you are low in vitamin A the Iodine might not be effectively absorbed.
The same goes for selenium. Excess Iodine can be toxic for your thyroid if you are low in selenium and vice versa.
I am still recovering from 1 mg iodine intake for 4 days. It gave me crazy tachycardia. I thought I was dying. It's been a year since and I am still not 100% recovered. My guess is that taking iodine disrupted my electrolyte ratios. I've been taking magnesium and other things.
So, yeah, I believe iodine sure does increase your body's need in other nutrients.
I also think that advising people to take crazy doses like 50 mg without medical supervision is irresponsible. And to think that taking mega doses of one nutrient disregarding what it might do to the balance of other nutrients is downright dangerous. Iodine doesn't work in a vacuum. Your body is a complex mechanism designed to work best with specific ratios of nutrients.