In th UK, riding fixed gear is well accepted as part of training for road riders. Long winter rides on a fixed gear are the traditional way of building aerobic fitness. Some very successful road time trialists use fixed gear to compete and win.
The standard fixed road bike has both brakes, it is definately a road bike with fixed gear, rather than a track bike let out on the road.
Fixed gear is more commonly used in winter and bad weather, often with fenders, because of its reliability and low maintainance. London bike couriers are esp fond of fixed wheel road bikes.