Apparently Lady Gaga is furious with Idol. They recut her performance and she claims totally ruined it. (see her twitter): Lady Gaga (ladygaga) on TwitterOriginally Posted by Misty8723;3895293;
And actually... while I usually think such claims are total ego... in this case she may have a point.
Here's the unedited performance and... it IS indeed VERY different.
Lady GaGa - Alejandro & Bad Romance live on American Idol - PerezTV
Some may still hate it, but its fair for her to say that Idol cut it significantly (by at least a minute and a half) and did change the flow of it a lot. For comparison... here's how it aired.
YouTube - Lady Gaga Live on American Idol: Alejandro (HD)!