If we approach this another way we will see that something must be wrong here. If we accept that the tap has 0 nitrate and we can not find any other source of nitrate in the tank, then we can work backwards from nitrate to ammonia.
160 ppm of nitrate, if it all comes from ammonia, means just over 52 ppm of ammonia was needed to make it. And if it is off the scale and even higher, then even more ammonia was needed.
I am still going with the testing error theory here. Too many things can effect the readings not including exactly how one shakes the bottle.
Typical of my persitent curiosity, I went looking for test kit comparison conformation. I found an interesting piece in The Advanced Aquarist comparing test kits. Unfortunately the test were done on sw tanks, however, for nitrate the API kit is the same for both and only the color cards are different. It is a longish article but it is definitely worth a read.
Aquarium Chemistry: An Attempt to Test Test Kits
By James W. Fatherree, M.Sc.
James Fatherree and Dr. David Flanigan asked hobbyists to test samples of the same water with multiple test kits. The results were interesting, with important lessons learned for both hobbyists and testing manufacturers.
http/www.advancedaquarist.com/2012/6/chemistry