That does not sound accurate to me.
Clay and clay substitutes are supposed to be rubbed over the surface with a lubricant. When used this way the ABRADE off the offending contaminants ON the surface, they don't remove the surface.
It's possible clay or a clay substitute could mar or scratch paint if dirty, contaminated or used carelessly, and scratches are "voids" in the paint so in this context they would "remove" paint in practical use they are not "paint removers".
Hard water is a term thrown around VERY LOOSELY. Technically what it means is water with dissolved MINERALS in it. Then when this "hard water" dries on a surface, (like car paint), the water evaporates and leaves behind the minerals which technically would be sitting ON TOP of the paint.
IF the water dries and it leaves an imprint ring or a crater etching, then this wasn't caused by the minerals but by other CORROSIVE substances in the water here on Earth.
Make sense?
Then if this is the case, that is you're are seeing imprint rings or crater etchings, then rubbing a clay bar or a clay substitute like a Nanoskin clay block, towel, wash mitt or pad, over the paint will not remove these types of defects. You must use a comound, polish or cleaner/wax and ABRADE the paint surface to level it to make these types of spots or defects visually and physically disappear.
Make sense?
Here's an example of a clay substitute...
Sounds like you're going to need to machine polish to remove these spots.