Is this why Futurama doesn't use the birthday song?

[EdenMaster]

Weird Al does get approval for all the parodies he does, although he doesn't necessarily have to.

Correct, in fact when he was misinformed by one of his people that Coolio had agreed to a parody, when in fact he didn't, he was mortified. If I recall correctly, since that incident, he's approached every artist personally about parodying their songs. Most of the time, the artists consider it an honor and are cool with it, and no he doesn't have to, but Al's just a classy guy that way.