The referendum was won because people were swung to the leave side by the case made by the leave campaigners. A case full of immediately demonstrable lies. If at least 650000 of those people were specifically swung that way by those lies or anything from 30 years of Boris Johnson's EU fibs, then the "they didn't know what they were really voting for" argument is sound.
This isn't about a metropolitan liberal elite thinking abstractly and paternalistically about swathes of poor people in The North about whom I have only heard through Ken Loach films.
All of the halfwits I knew at school (who I still know) voted to leave (I can tell because they post "Get Brexit Done" memes next to ones about councils banning Christmas and illegal immigrants being entitled to more benefits than pensioners).
That doesn't mean that everyone who voted to leave is an idiot, but if the lies of the leave campaign attracted 650000 more of them than the remain campaign did, then the leave result was artificially bolstered by people who genuinely did not know what they were voting for.