What vote in any democracy has not been surrounded by misrepresentations by advocates of different sides?
There was no censorship in the Brexit campaign. All sides were free to make their case for months during the campaign. There were plenty of false and misleading claims on both sides, as well as attempted debunking of these claims on the opposing sides. The Brexit debates were far more thorough, fair, and civil than anything you ever see in the US or most other democratic countries.
The notion that the electorate shouldn't have been trusted to sort through all of this, and requires a set of true facts cultivated by some elite group, undermines the entire premise of democracy.