A far more likely explanation is either poor testing that gave a false "all clear" while the patient was still sick. The tests are not 100%, that you don't detect the virus in the sample doesn't mean that the patient is not infected - it only means your sample didn't contain the virus. Which could happen for all sorts of reasons. That's why multiple tests are usually required - commonly two, in some cases up to eight consecutive tests had to be clean before the patient was discharged.
Or the patient has not been completely treated and the virus became dormant for a while, reappearing again later. This is known to happen with other diseases as well - e.g. ebola virus could stay dormant for weeks in the eyes and cause the disease to return again.
That said, the chief scientific officer has stated that this is likely to be an annual virus: https://www.telegraph.co.uk/news/2020/03/13/coronavirus-outb...
I found two other articles about the same case https://globalnews.ca/news/6623287/coronavirus-multiple-infe... and https://www.reuters.com/article/us-china-health-japan/japane... . t's not 100% clear, but it looks like a continuation of the first infection after a few week of no symptoms. It makes more sense than no immunity (at least at the short time), and a second independent infection.