My mother was concerned that some of her information, and mine, leaked because she signed up for another bank account from a place she decided she didn't trust. She said she wasn't worried about the money being stolen, but she was worried about our identities being stolen.

My concern was the complete opposite - I assume that my social security number and address are already for sale for a fraction of a cent somewhere, bundled with 10,000 other identities. But if money gets stolen, that's a whole rigamarole, with banks wringing their hands and saying "identity theft" as if that clears them from any responsibility.