I don't know how/why the "don't run the skimmer 24/7" myth started but I am expecting it was a result for reducing energy usage.... most likely for downdraft skimmers and the like with large pumps. Now with softie tanks (or where dirty tanks are preferred) the trick is not oversizing the skimmer, not turning a skimmer off. Still, skimmers are not 100% effective in removing all organics, even with multiple passes, so a skimmer does not remove all organics. Even then, for a skimmer to work constantly, there always has to be more organics in the water than the skimmer can remove. I am way oversize in my skimmer needs, 8" bodied MSX with a bubble blaster pumps which "rates me" up to 300g on a 65g. I still can't remove all organics, but at the same time, if I didn't feed as heavily the head eventually disappears (only after a long while with low feedings). Skimmers take time to build a nice head of organics and foam column, turning it off knocks it down and any organics left then dry and fowl the neck or re-enter the water. If you are going to stop a skimmer, then just go skimmerless. As far as removing Iodine, Iodine is a major component for algae growth and most iodine is sourced from harvesting kelp/algae anyways. I have no problem of the skimmer removing it especially, since most commercial salts are high is iodine from my readings. Skimmers do not remove any of the major "trace" elements needed for coral growths, they remove dissolved organic compounds. If the skimmate is wet, it will remove the elements dissolved in the water in the amount that is in the wet water.
The friend isn't crazy because there is some good "thought" behind it, it is just based on mis-information and misapplication of "skimmer theory"