Having a standing army doesn't prevent invasion. It's because we have an over abundance of well armed rednecks, gangs, mafia, etc. that are more than willing to put a bullet in an invader. Our army started as anarchistic militia, and that worked out pretty well for us, eh.
Our behavior on the world stage makes us more or less of a target. No standing army to invade other nations means we are traded with and liked better.
The Philosophy Of Liberty -