GoDaddy is very similar in that most all the emails they send are titled "ACTION REQUIRED" or another equally misleading alert. Very frustrating, builds nothing but distrust from me... like having a friend crying wolf every 10 mins.
I checked "don't automatically renew" when I first signed up.
I removed my credit card a month ago, when I realized it had been saved.
My father is out $500 for 3 lousy domains (typical name extension coms swindles) and the typical GoDaddy "premium" services, because GoDaddy managed to find his new credit card info without him entering it.
That is GoDaddy found out the new expiration dates for his card. Seriously, they can do that. There is VISA/MC program which merchants can use to obtain new credit card information from previous customers.
Of course, it is his fault for not explicitly cancelling the domains, but GoDaddy can be an expensive lesson.
More importantly, your dad shouldn't be out $500. I had some SSL certificates rebill through Godaddy at an astronomically higher rate, so I called, and was able to easily obtain a refund. If Godaddy isn't willing to offer a refund, just call your credit card company and issue a chargeback. The chargeback process greatly favors the consumer, and you're almost certain to win.