It may be that the request didn't make it to Lady Gaga until the full song was sent over.
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.
I thought the same thing as you at first, but perhaps Gaga might have taken issue with the short sound clip from Madonna's "Express Yourself" (at 1:58 in Weird Al's version). I think Gaga has been accused of copying "Express Yourself" and Weird Al is poking fun at that issue.
http://www.nydailynews.com/entertainment/music/2011/04/20/20...
People who work in the music production see a lot wider spaces inbetween subtle variations in sound than most of us. There are as many ways to construct a song as there are to construct a program, even if you know the "general idea."
Yes, but how does any of that affect the decision of "Yes, it's OK for Al to make this comedy song"? He's not asking her to put her name on it or positively review it — just to say she doesn't mind him doing it. So I don't see how "subtle variations" make any difference. As he said, this was the first time he'd encountered this in many decades of making parodies, so if you're implying that this is just how musicians work, you're wrong.
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?