I don't think anyone has claimed that Leave voters were of a single, unified voice. That much is abundantly clear, and is a point made increasingly evident with each passing day as we lumber between no deal, rejected withdrawal agreements, and ignored calls to scrap the whole thing.
What do you mean by 'the Brexit campaign'?
Leave campaigned for Brexit based on lie after lie, and a complete fantasy. Remain campaigned against Brexit with warnings of negative consequences which were all seemingly founded in reality.
It's not at all comparable to put Remain maybe asserting something that was only a possibility (no matter how real that possibility was), and Leave literally making things up to win votes.
It wasn't the job of Remain to paint a clear picture of what Leave would entail. Remain's job was to deter people from wanting to Leave, and they attempted to do that by warning people of the possible, but extremely likely, negative effects of a Leave result.
Leave should have been the ones painting the picture of what Leave would entail, but in the three years since the result, we've gone from £350 million to the NHS per week, amazing trade deals with every country in the world while maintaining a great relationship with the EU, and closed door to unwanted immigrants, blue passports(!), and most importantly, absolutely not leaving without a deal, to stockpiling body bags for an increased mortality rate, hopefully having enough food, becoming only the third country (alongside Algeria and Serbia) to trade solely on WTO terms, increased immigration from non-EU countries, and a 'strong and stable' government with no control over parliament and no ability, or apparently inclination, to actually try and get any sort of deal done.
But yeah, Remain saying something "will" happen when really they should have said it "might" happen is just as bad.