Not the BBC, but you've reminded me about my least favorite bit of "fake" "news" from the Indyref: the government's Buzzfeed propaganda account. https://www.buzzfeed.com/youdecide2014
Apparently there were "no costs" associated with this, which is even harder to understand. https://www.parliament.uk/business/publications/written-ques...
Would probably make a good test case for anyone's "fake news" detectors.