Haha, hell no! Many people absorb what the media says with barely any questioning. Take this article for example, why is there no suggestion of Remain voters switching to Leave? Perhaps it's because the media coverage has been so one sided there's very little chance many people who voted to Remain would have need to question their convictions.
All the most one-side media coverage was on the Leave side, wasn't it? The Sun, The Daily Mail and The Daily Express in particular -- the main mass-circulation tabloids -- were full of pro-Leave lies.
These are also papers that, not coincidentally, hate the BBC for being independent and excellent value for money.
Really? What do you have in mind?
Which mainstream sources have been more impartial?