Example: Someone opens a bank account using your information. That's fraud. Someone lied to the bank, and the bank believed them. That's the bank's problem. But by pointing at you and saying "Your identity was stolen" (using the term "stolen" to make it seem like this is similar to the theft of a physical object), it suddenly seems like it's your problem.
I agree that it's misleading, but have to concede that whoever first came up with that term must have been an expert in framing and spin. There are few words that so effectively distort the discussion as "identity theft".
But it is the bank, it should be! When a bank is robbed, its clients aren't the victims. The bank is. The clients aren't giving money to the bank for nothing in return; what they get in return is assurance of safety and availability (otherwise, that would be a loan, not a deposit). Spinning the failure to deliver on that obligation as the client's problem is indeed great PR work.