Aren't there two issues here? The copyright and the orginality.

Copyright then: Of course if a song/tune is only part traditional, you should cite your sources. This probably does only apply to people who are recording/well known/making money out of it; for the rest of us, it's only polite really, don't you think?

For your average folk club singer, I personally think that the originality issue is of greater importance. No matter how flattering, if you perform a note for note cover of a piece, ultimately you're performing a (probably)weaker version of something that your audience could listen to at home. If you can bring something new to it, no matter what your technical standard, you're a better musician for it. That's the point of live music.