Yes, he says that a lot. He's been screwed out of a song once where the artist wanted it, but the label objected so he stopped working on the song - I think it was later released as part of Squeeze Box or something because the artist finally convinced the label to approve it.FWIW, Yankovic explains that while he isn't obligated to get permission from an artist to parody their works, he insists on doing so, and if they refuse, he'll move on to something else.
It was also a problem during his early days. These days, artists WANT him to do a parody - it's a final sort of thing that says they've "made it". But he's only ever done one request (from Madonna - "Like a Virgin" to "Like a Surgeon") and that was because she shared the label with Al so was able to apply a little pressure that way.
Who cares if you got some music award, getting Weird Al to do a song based on yours is the ultimate exclusive award and so very few of them are handed out.
I have a DVD of Weird Al music videos - it was one where I had to learn how to rip a DVD audio track out so I could listen to it on my iPod back in the day.