Would she be pissed off at A) The bank? B) The browser? C) The computer? D) Her internet provider?
People can change browser more easily than changing banks. They can even have multiple different browsers on their machine, and one for only doing banking.
For many people, the icon on the desktop they click isn't important. They just know when they click that icon, it brings them to "the internet". If she's one of those people, my guess is she blames the bank.
