I do not know anything about the distilling process, but from what I heard years ago, distilled water can pick up metals as it travels through the process. If the distilled process involves copper or iron fittings, then it may be in the water you purchase. The only metal that ok in the aquarium is stainless steel.
Copper should only be in a quarantine or treatment tank when it is purchased as a liguid additive to treat disease.
The fish and corals are not exposed to metals in the wild at the concentration that may be in the distilled water.
It's better for you and the tank inhabitants if you went to the lfs and purchase an ro/di filtration system.