Cecil’s 1985 column seems to over-exaggerate the danger of Anisakis a bit.
From the FDA’s website at http://www.fda.gov/Food/FoodSafety/FoodborneIllness/FoodborneIllnessFoodbornePathogensNaturalToxins/BadBugBook/ucm070768.htm
There are fewer than 10 cases diagnosed a year in North America (although the article acknowledges there might be more undiagnosed cases), and generally they are “eliminated spontaneously from the digestive tract lumen within 3 weeks of infection.”
ETA: Link to column: Can you get worms from eating sushi? - The Straight Dope