What they attempted to claim was rights to it being performed on television (and similar). If I'm sitting at home, I can sing whatever song I want. I can sing the entirety of Bohemian Rhapsody by Queen and no one would care (except maybe my roommates and neighbors). It becomes an issue of copyright when someone tries to then use that creative work, whether that include lyrics or melody (often called the composition) or any part of the recording (called the master). The composition and the master could be owned by the same person/group, or it could not. It depends on the contract set up for the song.

Note: Obligatory IANAL, I'm just an independent musician who at least vaguely needs to know about this stuff for my creative work.