In the United States, there already is a law: the Health Insurance Portability and Accountability Act (HIPAA), passed in 1996. It established a right of patients to their health information on demand from their healthcare provider (with some exceptions, and allowing the provider to charge for copying or transmission). As @theGig said, people just need to demand it. The culture of health care providers is paternalistic, though, so they’re not inclined to give out data without being asked.