You are reasonably right, and the statement copper is toxic and will cause vomiting is correct if drunk in quantities. .1 PPM is still a reading and will not cause ill health, in fact people wear bracelets to ensure that some copper is going to enter the body for health benefits.
If you put a piece of copper in to standard tap water, you will see a rise in copper solution in the water over time.
My statement still stands, if you want to be assured that the water you are using for any aquarium system is suitable, you test prior to using.
If you have copper susceptable fish, then you should be testing for copper. You probably will not get a reading to worry about. However you need to be aware and test prior to usage!