Leaving fish on ice a day or two might improve texture and taste, but it has nothing to do with killing the parasites. Here is some interesting reading on the subject:
http://www.fda.gov/Food/GuidanceComp.../ucm091704.htm
The important stuff:
Freezing and storing at -4°F (-20°C) or below for 7 days (total time), or freezing at -31°F (-35°C) or below until solid and storing at -31°F (-35°C) or below for 15 hours, or freezing at -31°F (-35°C) or below until solid and storing at -4°F (-20°C) or below for 24 hours is sufficient to kill parasites. FDA's Food Code recommends these freezing conditions to retailers who provide fish intended for raw consumption.