It's a strategy that Putin and Trump have used effectively. Make false statements and lie to muddy the waters so much that people can't keep track of what's true and what's false.
Seems to be quite effective.
There's a French philosopher, whose name I forget, who basically argues that some people judge a statement by its truthfulness, and others by the sincerity with which its uttered. I suspect for many Trump/Brexit supporters, the latter is the lens through which his comments are viewed, hence why so few of his backers have changed their minds, even after he has lied more frequently than any president in American history. What he says doesn't really matter to them. This is almost the philosophical version of his shooting people in Times Square comment, as he knows he doesn't have to speak the truth, just speak with conviction and never back down on his stance. If he does that then people will no more abandon him than you or I would abandon Everton because they're crap.