Do they research, or just enforce on behalf of their members? There are lists on some sites (in the US) of songs which are known to be OUT of copyright (in the US), and which contain may old English songs. I don't know of a site which tries to list songs which are IN copyright. I suspect it would be an impossible task. What exactly do you want to know?
a) whether a song is in copyright or
b) who currently owns the copyright or
c) who originally wrote it, in order to attribute it?