Whereas it's true that any water you add will eventually come to an equilibrium of dissolved solids, distilled water will absorb more.
Whether that means anything?
I have yet to hear of a single case where distilled water actually caused a problem relating to mineral deficiency. Mineral deficiency issues are usually very intangible and may be attributed to any one of many causes.
In this day and age of vitamin supplement powder, it seems that our frogs are well vitamined and mineraled as it is.
Furthermore, the coconut media itself contains minerals; perhaps it is absolutely 100% unnecessary to use mineral water in this case because of the minerals in the media.
So I bet you are correct that distilled water is fine for this purpose.
But since mineral water is sold along side distilled water at the store, I purchase both.
There should be a brand of gourmet "spa" frog water. You know, with a consistent scientifically proven purity to promote maximum health and well being. Eh. There probably is one already.