I am a paramedic. I take care of people in very compromising positions (most people don't worry about getting dressed if they're having a heart attack at 2am). I worry that _their_ privacy needs to be protected.
This also isn't simply about 'modesty'. There are many ways medical information could be used against someone (denied a job, denied housing, denied various forms of insurance, etc...). There are many reasons personal medical information needs to be protected.