Standard table salt typically has iodine added. It also has a chemical added to make it pour easier. This may not have a notable impact on a healthy person, but if you genetically misprocess various things and are medically prescribed a high amount of salt, that double whammy seems significant to me. You are consuming a lot of these extra chemicals and no one is questioning what that does to an already wonky physiology.
I no longer purchase Celtic Sea Salt. It is no longer necessary. But I still avoid standard table salt and favor brands that list sea salt as an ingredient.
Wikipedia: "Worldwide, iodine deficiency affects about two billion people and is the leading preventable cause of intellectual and developmental disabilities."
Wikipedia also lists sources for this claim.
Edit: if anybodys doctor told them to be careful with iodine then they should listen to their doctor instead of listening to random strangers on the internet. I'm just pointing out that there is good reasons why we started adding iodine to salt.
As far as I know, there are no studies on how consuming those additives in high quantities impacts this population with a genetic disorder that causes them to misprocess a number of different things.
It's not on its face impossible for sea and rock salt to differ in trace minerals, but be aware that the salt itself is the same in both. From the medical stuff you mentioned it sounds like it's the salt itself that's having the beneficial effect and not the other minerals.
Although, I do see an oft-overlooked wrinkle to it: the costs of these minor changes are so small that the odds that there might be something going on unknown to medicine might be worth taking.