Isn't all media skewed one way or another? Our mistake is to believe that its output is what we should think.
It's partly why I voted Remain. Yes, I thought it the better option, but even if I'd believed otherwise I would have voted the same. The whole journey between announcement of the referendum and the vote was biased, politicised, and often downright false information, from the £350m Bus of Lies to... well, pretty much everything, from all political parties as well as the media. Very few of us had a true picture of what the EU really is.
Put it this way. If I was the curator of some huge stately home in desperate need of renovation, I might have enough knowledge to narrow down its fresh look to style A or B. Would I then call in a team of architectural and design experts to decide, or go down the pub and ask my mates? They would know about as much as many of us knew about the EU.