Firstly, publishing rights aren't always owned by the band themselves. The most famous example of this is probably The Beatles' publishing rights, which were bought by Michael Jackson, and then Sony. Every time Paul McCartney plays a Beatles' song live in his concerts he's going to have to pay some money to Sony, even though he co-wrote it!

Bands that do own publishing rights typically set up a limited company to administer them, and songs are frequently co-written. Bands are often obliged by these various agreements to effectively pay themselves (minus the administration cut, etc). The article linked to seems to suggest that Led Zeppelin either co-own the rights with Warner-Chappell, or have them administer them on their behalf. Either way, they'll want their appropriate cut!