According to Wikipedia, it included Jon Bon Jovi, Steven Tyler, Joe Perry, Jonathan Cain, Deen Castronovo, Richie Sambora, Alec John Such, Slash, Steven Adler, Rick Marty of Alice Cooper (and apparently a zillion other bands, I can't seem to find much on him, picture-wise), Tommy Lee, C.C. DeVille, Rudy Sarzo, Billy Idol, and Ratt.
we can eliminate keyboardist because he was allowed in the video.
I feel like it must be someone from Idol's band, but not sure who. I'm not real familiar, and the searches I came up with for band members from that time period, don't help much.