There is evidence coming from China that people who had the virus and recovered became re-infected. Which means there is no certainty at this point on immunity.
I am aware of that, but there is still doubt in that data. Apparently the tests used in a lot of Chinese people have really bad false positive and false negative rates, so it could lead do conclusions such as apparent reinfection. We'll have to wait and see if it happens with more people, especially in regions with more accurate testing.