Iodine is talked about with regard to the thyroid because some people think that's the only reason we need iodine, to make thyroid hormones T3 and T4. The "3" and "4" refer to how many atoms of iodine connect to the amino acid tyrosine. But, there are iodine receptors throughout the body. So, on this forum, we prefer to think of iodine as part of what's necessary to have a healthy body, not just a healthy thyroid.

The answer about cholesterol and iodine was in the paragraph above the one you quoted. Luckily Dr. Wright wrote about it, because I'd sound like an idiot trying to explain my haphazard grip on this stuff :)

"When I was a pre-med student at Harvard University, the famous chemistry professor Louis Feiser made a point of demonstrating to all the pre-medical students that iodine and iodide would make oils, fats, and waxes (cholesterol is actually a wax) more soluble in water."