I agree with Anahata - there is a difference between copyright of the song itself (which you can't do for a traditional song) and your recording of the song (which is protected by law from illegal copying).

But as Bert says, the purpose of a demo is to spread the word and hopefully get bookings etc., so why be too precious about it? You (presumably, anyway) want as many people as possible to hear you, so if they copy a demo and pass it on, that's good news for you (or should be).