In an electronic world, someone pulling a similar trick likely would get caught. Systems log who gains access to a record.
But such thefts could happen more easily on a grand scale. Instead of walking away with a backpack of records, it becomes possible to take off with virtual truckloads. Doctors and hospitals and the vendors that create the systems that store electronic medical records have been working on preventing breaches and protecting privacy.
Meanwhile, the same safeguards put in place to keep the world from learning you have a history of mental illness or are at a high risk for uterine cancer might make it harder to deliver critical information about your health to an emergency room physician.