What prevents the user from selecting a different video and who is the arbiter of 'what makes sense and what doesn't?'
I suppose those can be rhetorical questions, if you want. To be clear, I suspect I hold very extreme views on the concept of free speech, at least from your perspective. Lest you read too much into that, the speech I'm defending sometimes comes from people who would harm me simply by virtue of my not being white.
In this case, the lady is a journalist. Her reporting included extremist videos. You're saying YouTube is not the place to share investigative journalism because it's highly destructive hate speech.
Youtube has rules about the content they are willing to host and she knowingly violated those rules. Who she is any why she did it shouldn't come into it.
No, it shouldn't matter who she is. It matters that the rules are Wrong.
And no, I'm very much okay with the Muslim posts. In fact, I've watched many of them. The ISIS recruitment videos are well made and have pretty catchy songs.
Obviously, there should be a place, similar in price and ease as YouTube to where she can host such things, but YouTube is not the place. Ideally the new system will be set up to weed through what makes sense and what doesn't.