I know for a fact that most tests used in the pet industry will read both ammonia and ammonium as ammonia, so you can get false positives even with otherwise accurate tests.
Most ammonia tests use a Nessler reagent which will register ammonium as well as ammonia. If your water has chloramine instead of, or along with, chlorine, you'll end up with false positives. As more and more municipalities use chloramine, it's coming up as an issue more and more.
Chloramine is made up of chlorine and ammonia. It is the bane of fishkeepers for a couple of reasons.
1) It doesn't evaporate out. Ever. Back in the day, all you had to do with water was let it sit out unpressurized by the pipes, and the chlorine would evaporate out, making it safe for fish. You can let water sit out for a month, but chloramine HAS to be detoxified chemically.
2) Water conditioner that treats chloramine as well as chlorine breaks apart then binds the chlorine and ammonia into fish safe compounds, ammonium being the ammonia portion, which still registers on any Nessler reagent ammonia test.
Nessler reagents are used in almost all pet industry test because of two things, accuracy and the fact that it's cheap. Non-Nessler reagent tests are available, but most are around $100. The cheapest I found was about $30 plus shipping and I can't vouch for it's accuracy, I've never used it.