In some cases the account officially belongs to a company so the real person is only an agent in any case.

Also there are attorneys: a real person acting on behalf of a different real person. Currently many financial institutions seem to be unable to cope with this situation. When talking to a call centre, in practice it's much easier, and probably not illegal, for you to impersonate the person you're representing rather than attempt to explain the actual legal situation to the confused employee in Bangalore.