This isn't just a problem with websites and the internet. Your private medical data at a doctor's office or clinic is accessible by any number of underpaid, un-motivated office assistants, medical assistants, etc.. Hell, I bet the janitor could get your records if he wanted to. I've heard stories of people trying to use medical records to blackmail patients. Maybe someone who works at your doctors office is also your neighbor, and they're jealous of your swimming pool. Some psychopath might just take your medical records and tell the whole neighborhood how you have herpes or an irritable bowel, just to hurt you, no other reason.
The problem with any security is that its always monitored by humans, and humans are always susceptible to greed, anger, jealousy, stupidy, insanity, etc... Think about that the next time some cop pulls you over for speeding, you better hope his/her spouse wasn't just caught cheating on them.