That's right.
There are two other ways: live plants absorbing them (which you don't have right?) and a process called dentrification (if I have that term right, Eco would know) but it's usually not worth mentioning (again Eco lol).
Just for kicks you could test your tap water, although if you have high nitrates in your tap water you should contact the EPA or something.
The nitrate test is easy to get wrong; I did it once and get 0 nitrate when I had 40 before and I shook the bottles and banged them and did everything as usual. I repeated the test and got the right results. Are you shaking both bottles? I usually do, even though the test kit says only to shake #2.
I wouldn't worry about it. As long as ammonia is dropping and nitrites are there let's continue and see what happens.