Brexit has been brought into everything, because it could effect.... everything. Pro remain? Don't take the piss! They've been terrified of annoying the extremely vocal minority of brexit supporters whose constant mantra seems to be 'stop going on about brexit', and 'just get it done'.
Just because some people cast their vote and expected, whatever the hell was their own personal vision of brexit, to just be done without fuss, doesn't mean that the BBC reporting on the unfolding shit-show of the next 4+ years means they are pro remain. Honestly, most of them really try to achieve impartiality. But it was like attempting to be impartial reporting on climate change or flat earth thoeries. Of course at times they are going to make brexit supporters look stupid, simply by reporting what they've said. But when the tories are putting out tweets with an innacuracy rate(to put it kindly) of 88%, they simply didn't find time in the day to be correcting it all when they had so much Corbyn bashing to fit in.