This doesn’t account for it because South Korea didn’t even have the number of serious cases that Italy has.
The real answer is simply that the number of tests is not equal to the number of cases.
The number of positive tests is a factor of the number of tests done, and how selective the testing was allowed to be. It is only loosely related to the number of infected people (technically it is the lower bound).
My comment was directed at age structure of population accounting for difference in mortality, complicated by effective collapse of medical care in certain regions of Italy that meant severe cases that could have been managed because critical and then fatal without ventilation support.
The real answer is simply that the number of tests is not equal to the number of cases.
The number of positive tests is a factor of the number of tests done, and how selective the testing was allowed to be. It is only loosely related to the number of infected people (technically it is the lower bound).