It's nice to see PBS Idea Channel try to tackle the issue of online privacy. There are certainly those who will claim that you do make this choice when you use technology, but I tend to agree with Mike that the choice isn't as simple as it sounds and in some ways isn't really much of a choice at all (unless you're OK with cutting yourself off from a lot of the ways people interact with each other nowadays).
One nit pick, though, is that although Mike framed it this way, it's not the Internet that's necessarily insecure, it's computers themselves that are necessarily insecure. As the infosec saying goes:
If it runs software then it's vulnerable. If it's connected then it's exposed.