Distilled water should, in most cases, be fine.
That said, I am not comfortable stating that there are no readers of this thread who might encounter distilled water made with copper piping, and I'm not sure how one could make that conclusion.
If the distilled water was made on a device using copper cooling coils, that could be a concern, and most people would not know how their distilled water is being made.
When copper is used, there is copper in the product water. It has been measured and reported in the scientific literature:
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC437257/?page=1
DO any commercial plants use copper?
Well, they certainly use copper-nickel alloys when seawater is the raw material for the distillation plant. Is any of that product water sold commercially as distilled water rather than just drinking water for the local population? I do not know.
Here's a paper on desalination plants that currently use distillation to produce drinking water, and they commonly use copper-nickel alloys and they report copper in the waste stream (no mention of the product water, since this is a study of environmental effects, not the product water):
https://www.google.com/url?sa=t&rct...r0H-pFD5QjQIkYerIPrBFA&bvm=bv.113034660,d.cWw
"2.7 Heavy Metals
Copper-nickel alloys are commonly used as heat
exchanger materials in distillation plants, so that
brine contamination with copper due to corrosion
can be a concern of thermal plant reject streams.
The RO brine may contain traces of iron, nickel,
chromium and molybdenum, but contamination
with metals is generally below a critical level, as
non-metal equipment and stainless steels
predominate in RO desalination plants. Copper
concentrations in reject stream are expected to be
in the range of 15–100 μg/L.
and here:
http://www.copper.org/applications/marine/cuni/applications/desalination_plants/
"Multistage Flash Desalination is a heat exchange process and although many materials have been promoted for the heat exchanger tubing, copper base alloys are still favoured since they have given good service in these plants. "
and here:
https://www.nickelinstitute.org/~/M...elAlloys_PropertiesandApplications_12007_.pdf
"In the heat reject section the preferred allow is a 70/30 copper-nickel containing 2% iron and 2% manganese for best corrosion resistance..."