There are a number of products with "government approved lies." For instance, labels like "zero fat" may mean "less than 2% fat."
Some people on this board say that you can legally label non-distilled water as "distilled" in the US as long as it meets certain purification standards.
I haven't been able to verify this. (yet.)
This page seems to indicate "distilled" means distilled, but maybe the 127 million other pages of government regulation have other definitions.
As best as I can tell, it can't say "Distilled" unless it's actually distilled. The Walmart water I get says "Produced by Steam Distillation, Carbon Filtration, Reverse Osmosis, Ultraviolet Treatment, Microfiltration, Ozonation." Note that it doesn't say "and" or "or," so it's not clear whether it means all of those, or some of those.
It would make a lot of sense to do filtering, reverse osmosis, and microfiltration before distilling. That way, you'd get less crud buildup in the boiler for the distilling process. When you distill water, any minerals in the water will build up in the boiler and you have to clean them out. They may very well do all those processes except distilling for their normal "purified" water, and then use that water to feed their distiller.
The package also says "Premium Waters, Ft. Worth, TX."
By the way, "distilled" doesn't mean "100% pure". Most minerals and salts will be left behind in the distillation process, but certain chemicals such as alcohol, gasoline, and many other solvents will pass through the distillation process to some degree.
The big "germ" advantage of distilled water is not that that it's germ free. The advantage is that even if germs fall into distilled water, there are very few nutrients for them to eat and build new germs. For instance, germs require nitrogen compounds to make protein in order to reproduce. In pure water, there is little to no nitrogen they can use, so they can't reproduce. Germs that fall into distilled water may live, but they usually can't reproduce.
(Yes, there's nitrogen in the air, but most germs can't use it. )
Germs can grow in your water tank or water jug if nutrients fall in from the air flowing through the machine, leach out of the bottle, or if you use some kind of cleaner that leaves behind a residue. For instance, can the germs use some sort of residue from the liquid dish soap you use to clean your tank?