On what grounds would she reject the song, but be ok with the lyrics? Because by asking him to sing it she's basically said "I'm ok with the words. But I might not be ok with the delivery."
Delivery can make the difference between affectionate parody and harsh parody.
Most of Weird Al's songs don't really make fun of the original performer. Most of 'em are really about food, or surgeons, or the Amish, or the Beverley Hillbillies. Only a couple of 'em actually target the perceived flaws of the actual singer (e.g. his version of "Smells Like Teen Spirit" which makes fun of Kurt Cobain's somewhat incomprehensible drawl).
This song did strike me as a little more critical than most of what I remember (though Smells Like Nirvana did come to mind), but hey, that's obvious from the lyrics. I wouldn't fault her for saying no at that point; instead she refused to respond until he'd done the recording.
So I agree with Al, it was a stupid demand to make (especially considering that she should know that recording a song isn't cheap), and Al's reaction isn't really about the money; it's about punishing her for either thoughtlessness or meanness, and also a bit about getting a bit of press for himself.
I suppose I'm not terribly impressed with either of them.
1. The lyrics to the song
2. The music to the song
3. What Al sounds like when he sings
What about the actual track could be "a lot different" from the information she already had, to the degree that it would lead her to withhold approval she would otherwise have granted?
Think about it from the assistant's point of view, who reports to Lady Gaga. He doesn't want to take something to Lady Gaga and have her say, "Mmmm.... I don't know" and have the issue unresolved. Meanwhile, it costs none of his own effort to ask Weird Al to send over the recorded song, which he can then take to Lady Gaga in its entirety.
http://www.nydailynews.com/entertainment/music/2011/04/20/20...
Al is being a bit disingenuous with the whole "I respect the artist's wishes", but then releasing the song and banking on the Streisand effect to do its magic. You can call her out on screwing you over, but don't play like you don't know what you are doing.