Distilled water has no minerals, most spring water actually has way too many minerals. Every source is different though, I've seen bottled water with pH of anywhere from 6 to 8.2 (totally unrelated to mineral content). Different all over, but pretty much every natural source contains minerals.
Was the middle test done on water from the tank? (if you are still interested in what's going on here, that is).
I was always under the assumption that the ammonia component of chloramines would be read in tests, but maybe not considering that it's not "true" ammonia in that form. . .
About chloramines.. NH2Cl is broken down to NH2 (ammonium) and Cl gas (removed by conditioner). Your pH reflects the path the ammonium takes. In pH 7.2+, ammonium will convert to ammonia (NH3-- the bad stuff). In under 6.8 it will remain ammonium (not as bad stuff). . . The middle range is generally a mix of ammonia/ammonium. Ammonia/pH is a chemical balancing act. . . Don't fully understand that aspect yet and don't have chemistry again until second semester.