"insure": Provide insurance coverage. Arrange for compensation in the event of damage to or loss of (property), or injury to or the death of (someone), in exchange for...: "the car is insured for loss or damage"
"ensure": Make certain that (something) shall occur or be the case.
I think I have found an explanation in http://articles.latimes.com/1998/jun/17/food/fo-60599 "and forget the fact that "insure" was nearly always spelled "ensure" in the 18th century."
It is probably one of these things where Americans swung one way and Brits the other. Another example is http://en.wikipedia.org/wiki/Aluminium#Etymology where Americans use the original British spelling and the Brits use the original American spelling!
But insure and ensure mean different things - they can't be interchanged!
Not sure if it's something unique to my upbringing however.
Holy mackerel, you're right:
https://www.google.com/#q=site:newyorker.com+insure
At first I thought, "Well, but the New Yorker does have a few quirks" - but the analogous search for the NYT shows that they do it too.
I always assumed "insure" for "ensure" was a sign of illiteracy. What's that thing called in psychology where the brain edits out incongruent things and just doesn't see them? I must have been doing that with "insure" for years.
"https://mysocialcloud.com/aboutus In addition, our site utilizes advanced encryption to ensure your information is always secure"