I don't think so. The reason he got fired might not have specifically been the video being posted. The video was just evidence of a whole bunch of violations. He probably wasn't supposed to let anyone else use the pre-release X, or let anyone access his confidential Apple material even if it was on a non pre-release phone, or take videos at the Apple facility. The only way it would have been OK was if she did it after the phone was released, on a private phone that didn't Apple business materials on it, and then no permissions would have been needed.
But the troubling part is this young lady doesn't seem to understand that its not OK to put everything on YouTube. This latest video explaining that here father was fired might also be a problem. Usually with terminations like this there is some kind of separation agreement that has some terms like, we won't prosecute your or sue you, we'll give you a few bucks as you are leaving, and you agree to never talk about this. Now his daughter is out posting a YouTube video about it again. This could have violated a separation agreement.