Daniel Suelo, the subject of the book, has not had health insurance for those 12 years. He doesn't go to doctors, but has remained healthy, which he attributes to lots of exercise, eating relatively healthy, and most of all, not worrying. He told me that if he spent all his time worrying about how he might get sick, he would likely be out of emotional balance, and would be more likely to become sick! As for me, I hear you about the fear. I personally am afraid to let my insurance go, too, for fear I'd get sick and lose my house, or worse yet, my parents would lose their house to pay my bills. Ultimately what this book is about is that fear: how has this one person managed to live in a scary world without being afraid.
By the way, here's how Suelo himself responds to that question:
https://sites.google.com/site/livingwithoutmoney/Home/10--what-happens-if-you-get-sick-or-injured