Don't immediately assume that Gaga didn't want this to be released. I suspect she knows full well that refusing someone like Weird Al will result in more press (negative or otherwise) and more attention for both of them - the good old Streisand effect coupled with reverse psychology. Despite enjoying Weird Al in the past, I haven't listened to any of his new tracks in years but I've heard this one now..

It'd only take Gaga to 'conveniently' change her mind in a few days and the Internet hype machine could have done its job, promoted Al's album, promoted her image yet more, and everyone's happy.