One should, I think, remember that if 2% of the voters went the other way things would have been very different. So even if your suggestion is true (it isn't), what really matters was the swing voter.
People are essentially pluralistic. They liked the idea of this 'taking back control' stuff but they needed a certain amount of reassurance that things weren't going to go too pears, which they received in spades. Did some people kind of know they were being sold a pup? I am sure some did....which is why Gove of all people can be all like 'c'mon guys, you knew all along we were bullshitting you right? Surely you weren't that stupid?'. I mean even to this day, you get intelligent Brexiteers on Twitter taking Boris Johnson's words at face value and the cognitive dissonance involved is a sight to behold. There's some on this thread too.
Remainers didn't necessarily know what they were voting for (except, as mentioned, their continuing right to live and work in the EU), but I think a lot of them knew what they were voting against quite well.