From what I've read, this problem only seems to exist for Rogers and Fido customers in Canada. Even if you have the annoying "Who Called" feature turned off, there is still something else that sends an SMS message saying "1 new voicemail." That means I get 3 notices from the iPhone: 1 missed call alert, 1 VVM alert, and 1 SMS new voicemail alert. If you haven't turned off "Who Called", you get an additional SMS alert about the missed call.
I've talked to at least 8 different Rogers CSRs and iPhone support people, none of whom can figure out how to turn off the SMS new voicemail alert. If anyone succeeds in getting Rogers/Fido to turn this off, please let me know the solution!