Think of this way: what if you could simply stop paying rent when you want to move out of an apartment? Or you just stopped paying your cell phone bill when you want to cancel it? What if you forgot to pay your health care premium and you lost your health insurance??
Clearly these aren't acceptable ways to break out of a contract.
The author's trick to "lose" your card to prevent auto billing is inviting issues like this. It seems so much smarter to just check your credit card statement each month. That would be much less work than having to update your credit card number everywhere you do want to renew a service.
Your credit card failed processing and Zipcar kept your service up and prompted you to update the card. That seems like a great way to go. If they had simply cancelled your account, I could imagine this blog post going the other way. "I forgot to update my card and zipcar cancelled my account, leaving me stranded when I really needed a car!!"
With critical accounts like your car, apartment, cell phone... it seems best to be explicit when you want to cancel your account.