An interesting, and very timely thing to be thinking about! Network Security is always one of those "we should have that" things until such time that you really NEED it. 20/20 hindsight.
A better place, instead of the NY Times general article/summarization is to go straight into the stuff. Check out http://www.whitehouse.gov/CyberReview/ and you can download the PDF of the actual directive or watch some semi-useful video clips about people talking about this (what we consider) obvious state of affairs!
Is anything safe? Depends on who's after you! Where there is a will, there is a way. Most attacks are inane (different than benign) in nature and have no particular target other than that of convenience. While irritating, that's not the big threat. The people who KNOW what they want and have time to k ill, that's the real problem.
Are large systems secure? nope. Are the critical pieces/points secure? Kinda, but depends again on the details. The "internet" per se will remain in place. IMHO, nobody will k ill that, because that's the vehicle used to attack the actual targets. There may be "distraction" attacks though, but that's looking at CyberSecurity from the point of view of military or tactical planning (e.g., if I were a hacker, what would I do?).
The part that scares me more is the fact that some systems are even CONNECTED to the Internet. The nuclear power plants internal systems... What the #*$# were they thinking?