[bloak]

"in the case of a live stream on Facebook that's the user"

You need to argue that rather than just state it. I can see arguments for and against the proposition, but the facts that Facebook attaches advertising, sometimes removes content, carefully tunes their platform to maximise "engagement", and the user has no direct relationship with the receivers of the live stream, do rather suggest that Facebook is the publisher and the role of the user is more like that of someone who writes a letter to the editor that gets published in a newspaper - except, of course, that Facebook is publishing nearly everything, but I don't see that that's a fundamental difference.