snapped 2 brake cables in about 23000 miles of riding my during 2nd and 3rd years as a messenger, both times I was on a SS road bike front brake only
biggest danger isn't the snapping of a brake cable, its over braking on a slick surface while turning and dumping yourself on the pavement, which can happen on any bike, just like on a fixie its always a bit shocking the first time you break the rear free when not being ready for it