This is not true. RCD devices are designed explicitly to detect leakage through PEOPLE instead of the earth wire of the device that has a fault. They measure the current difference between active and neutral and if it's more than about 5mA then that means there's 5mA escaping somewhere and it shuts off.
Originally Posted by MartinP
They absolutely do not require an earth wire. They are to protect you when the earthing system fails or if someone tosses a hairdryer in your bath.
In AU, all houses must have an RCD in the main distribution panel and if yours does not, then adding one is a good idea. Failing that, you should use a portable/plugin one for anything that's in a wet area, because water is the greatest electrocution risk that these things can help you protect against. The RCD must be between the supply and the device being protected so it's no good having a portable RCD in an adjacent powerpoint, it must be directly in the lead.
Edit: looks like I'm a bit late to that party.