“….those tiny spots are like tar spots. You can’t wipe it off easily, need to rub really hard or scrap with finger nail. Gave her our info... any suggestions?”
Although it is obvious to you the problem is not caused by the wash, it is not obvious to customer unless customer has prior knowledge of problem as in being deceitful.
So, first thing is to identify potential causes.
Road tar can get on vehicles when it is first applied (overspray) or immediately after before it cures completely (splash).
Tar/asphalt overspray will look like little uniformly shaped dots. Splash can leave spots but usually it takes form as small irregularly shaped globs and smears.
Since tar/asphalt has molecular weight (heavy), splash is usually not visible above wheel wells.
The marks could be industrial fallout (i.e. railroad dust). However, unlike paint and tar, railroad dust will actually penetrate surface of clear-coat and begin to oxidize leaving a small discolored halo surrounding the particle. Since gravity is vehicle, railroad dust is usually seen only on horizontal surfaces, not vertical.
The spots could be mold (microbes) but mold tends to grow quickly into colonies (widespread) and eventually spreads into patches. Moreover, mold is not difficult as paint to chip off with fingernail.
So, my guess is industrial paint overspray.
Test it. Take a shot glass full of paint thinner and put a couple of the black spots in it.
If the spots breakdown and dissolve, its paint.