It's pretty funny that on one hand you say security is a big issue but with the other you are frustrated they haven't moved away from paper fast enough. Paper based systems when used correctly can be very secure. That being said they aren't without their issues e.g.
http://www.databreachtoday.com/800000-penalty-for-paper-reco...
Security is of paramount importance however never at the cost of digitization.
Imagine two scenarios
1. Patient diagnosis delayed or incorrect, if doctors cannot view the blood reports for next 21 days or doctor makes mistake since he cannot process data like a computer would.
2. The icu system got hacked on which someone's life depended.
I don't think you could choose one over the other.
A lot of the time, we trade off between convenience and security. However that is a prudent and deliberate choice.
What I see more and more happening is a reckless and inadvertent choice.