short circuits aren't the problem. A 16g wire can carry HUGE amounts of current for a short amount of time (enough time for the circuit breaker to open). It's overloads that are an issue. If the compressor seizes (for example) and draws higher, but not huge currents, the breaker won't open right away and the wire could fry. This is why protection should be used that is sized properly to the conductor size.
But like you father said, it's a rare chance and for our applications isn't really an issue.