It doesn't happen only if you put a passcode on your iPad, by the way. I have my iPad plugged into my computer, and had just finished backing up my iPad (thankfully) so that I could get the latest software update. During the update, I was prompted on my computer to "allow access" to my iPad. I clicked continue like a good Apple customer, and a new window popped up in iTunes that says "To allow access, please respond on your iPad..."
My iPad is stuck on the screen with the Apple logo and the progress bar (which hasn't moved in over an hour, by the way).
So, don't be so rude when you don't actually know what's going on. It is, in fact, a software glitch of some kind, and has nothing to do with her device specifically (or all of the other 140 people that have responded to this post alone saying they've had the same problem with their devices). I'm hoping that eventually the update will finish, and the iPad will give me the option to "respond on my iPad" so that I can allow access. I would agree with the suggestion from dwmusic, that iTunes should let you know that you can't actually give it access until the update is complete.