The best deal possible is a Norway-like arrangement, which would be unacceptable to nationalists.
You have no factual basis for claiming these people are asserting false facts or voting based on false facts. Brexit is a vote on what the future should look like, and no one has a factual basis to predict the future.
tl;dr people you disagree with aren't fraudulent by default
And in Trump's case (describing immigrants as "rapists" and "murderers") it is also demonstrably false http://www.wsj.com/articles/the-mythical-connection-between-...