I think using the word private is a bit misleading. Ground water is shared among all the well users in the area/water shed.
If drank only collected rain water then it would be private. Except for the pollutants picked up from the air.
If drank only collected rain water then it would be private. Except for the pollutants picked up from the air.
I do not believe my well shares water with their supply because they have much safer water than I do. We have many more heavy metals in ours, and more arsenic. They run off some basic water filters, and I have a much more complex water treatment system in my basement.
I'm not pointing this out just to argue - the point is that those of us on a well do maintain an awareness of where our water comes from and what is in it, probably much more so than those on public water supplies.
For the purposes of this discussion, unless one of your neighbors is pumping chlorine into the ground I think its fine. Also private vs public here refers to the ownership of the water infrastructure.