Yes, it can, it can also fall into the realm of inaccuracies with tests. "strips" are known to be inaccurate, and those stick on wheels are the worst.
However, bacteria does exist that converts ammonia to nitrite, which is even more toxic for fish. Another bacteria will convert nitrite into nitrate (with an A) which is the least toxic of the three. This 'cycle' is a necessity for long living healthy fish, however it is near impossible to obtain in small bowls. There is no magic number for tank size, but generally speaking anything less than 5 gallons isn't going to hold a stable cycle long term.