A bank transfer requires both parties to reveal their account number. I have been told by several people in both the US and the UK that this is a risky thing to do. In fact in those countries where there is no national register of residents and identifying oneself relies on things like utility bills that show your address rather than on a unique ID (personnummer in Norway) that a bank, for instance, can verify online they might actually be right, or right-ish at least.

I rarely hear of identity theft in Norway where banking relies on common ID services (BankID for instance) and the folkeregister (population register) but it seems to be a major problem in, for instance, the UK where there is no equivalent.