If the air is really clean, you have this part covered. But is it? It is not only about how clean it is where you live - that is, in your area, near ground level. Is it clean up to 2000 feet? Was it clean where water evaporated? What was in the air on the way? Start from reading about acid rains. And there is much more about this topic. Too much to put here. Rainwater most definitely is not the same everywhere.
Assuming it is clean when it falls, there are other factors. What is your roof made of? Glazed ceramic tiles are best for rainwater collecting as they do not contaminate water in any way. But if your roof is galvanized (zinc covered) steel, you may end up with too much zinc to your liking. If your pipes are made from brass, you will have a lot of copper and zinc. If your storage tank is made from plastic not meant for contact with food, you will have carcinogenic plasticizers in your water. And so on. And, of course, is your roof clean enough you would dare to serve dinner directly on it? And so on.
Maybe, just maybe, none of the above problems affect you. But you should check, carefully. In my country, chemical analysis of possibly drinking water is under $50. By our sanitary and epidemiological inspectorate. Find something similar in your area if you want to be sure.