She said something may have arrived in the mail about the insurance plan, but neither she nor her sister, who assists with most financial matters, saw a notice requiring an opt-out within 30 days.
There are a number of issues that arise here. First, it's remarkable that a product as sophisticated as accidental death insurance can be sold on the basis of a telephone handshake.
Moreover, because a bank has a marketing relationship with an insurer, payments can be automatically withdrawn from one's checking account without your having to provide an account number, thus making it much easier for people to end up paying for something they never intended to buy.
Finally, no signature is apparently required to seal the deal. If you don't opt out from the insurance coverage, the default setting is that you must want it. That's neither a fair nor a realistic standard for a business transaction.