With a single word in caps like that, I read it as yelling the word loudly.

The way it’s used here, by a PR conscious intermediary, it comes across more like bitter sarcasm. Like he would not let them release the statement on his behalf unless they yelled Facebook’s name when calling them out. It is similar to when a child tells their sibling they aren’t allowed to do something, but they say it loudly enough so that everybody understands the parent in the next room hears it too.