Nitrate is toxic to all fish. However, unlike ammonia and nitrite which can rapidly kill fish, the effect of nitrate depends upon the species, the level, and the exposure time. You want the nitrate as low as possible, and never above 20 ppm. Some fish, especially cichlids and many wild caught sensitive species, will react adversely to this level. Nitrate has not been all that well studied in aquarium fish, and the best way to think of the detriment is that the fish will slowly be weakened and stressed, and this is the direct cause of 95% of fish disease (the stress) so obviously the fish may eventually die from "x" or "z" but these problems might well be directly the result of the nitrate over time. Fish have remarkable capability to fight off many diseases, but in the aquarium they are immediately being hampered by all sorts of things, so keeping stress as minimal as possible is the aim.
Nitrate occurring within the aquarium is easy to deal with, as we have discussed previously in this thread. Nitrate in the source water is a very different issue. I will leave this as we have other members who have dealt with this issue and they can better explain it. AbbeysDad is one member who has had success dealing with high nitrate, and you could PM him to enter this thread.
Back to your fish losses...if nitrate was at 80 ppm which was a test number given earlier in this thread, and this or similar continued for several months, it would without question weaken the fish, making them more susceptible to various other issues. The ammonia was another possible; with high nitrate, ammonia would be more toxic than otherwise.
Re the API nitrate test...there are two regents. Regent 1 is added to the test tube of tank water, then you shake Regent #2 and then add drops and shake the test tube. When shaking Regent #2--the regent itself before adding the drops--shake it for a good 2 minutes, not just the 30 seconds it says in the instructions. Insufficient shaking of the Regent #2 can result in false readings. Regent #2 tends to separate in the bottle over time, which is why it needs to be well shaken before using it.