I heard similar claims about drinking distilled water decades ago, and determined that they were BS by self-experiment. Now, it does make a certain amount of sense that ion-free water could be problematic for biological systems, but distilled water is already close enough to ion-free (with respect to a typical biological system, which in some sense is just "very dirty water") that I can't see how further purification could possibly suddenly tip it from "just fine" to "so toxic it will kill a goldfish in seconds". In fact, form a biological perspective even rain water is pretty close to ion-free.