There's no reason why she can't stay, West's baseless accusations of her disrespect aside. It's taking place in a public place and he's a (crazy) public figure making a statement into a microphone at at public event. She wasn't being disruptive, she was standing there silently filming, as I'm sure others were. And those vets (especially the one at the end verifying that she's leaving) would do well to remember that it's her right to watch and videotape just as much as theirs. That's one of the (in my opinion) most important rights they were ostensibly fighting to protect during their service. But of course, because he's a Republican, the same rules do not apply.
Seriously, what an asshole.