This is not consistent with my lifetime of observations. For various reasons from pickling to sore throats, I've found myself making a saline solution from table salt and there is no sand undissolved at the bottom of the container. If I saw something at the bottom, and I always look, I'd think it was undissolved salt and agitate it till there was nothing, and then there is always nothing left, all dissolved salt.
The goal of iodine in mass consumer salt is a nutritional source of it, has nothing to do with radiation preparedness. Iodine rich foods tend to cost more than what the worker bees eat on a regular basis. I've possibly stated the obvious... kinda like why we have vitamins added to refined white flour, white rice, cereal, etc. The worker bees need carbs to do the labor and sweat doing it, so salt!