So I'd say that BLM is most properly defined as a social movement aimed at ending police violence and, to a lesser extent, doing grassroots work in black communities. I agree that many other things are done in BLM's name, but controlling the media isn't one of them. Unless you know something I don't.

The media reports on BLM activities, but BLM don't *influence* them as far as I can tell.

Social media is different of course, but that's made up of so many different individuals that it's not very meaningful to call them BLM. They're just sticking a BLM hashtag at the end of whatever they say.