I have no idea if these insurers can be trusted with $19/year, but it actually sounds like a pretty plausible business model. If you count up all the file-sharers on the net, and divide it by the all the fines and settlements ever paid to the RIAA, my guess is that it's way less than $19/year, which suggests that you could make a buck (or Kronor) at this. Link (Thanks, David!)
Update: Travis sez, "This article estimates the odds of being sued by the RIAA at 1:1840. This works out to a break-even point of $34960 per lawsuit."