To me it's kind of ridiculous to even question whether having constant access to your personal health records could make a difference in your health.
First off, people move, change jobs and doctors pretty frequently today. New patient intake forms are supposed to fill docs in on people's medical histories, but which would you trust more - a document containing all of your health details or your memory?
Second, having access to a document listing details like your blood pressure and cholesterol levels should make you at least slightly more aware of your health problems and might even change your behavior.
While I'm sure there would be downsides, including security concerns, I'd bet the positives end up outweighing the negatives here.