To be fair the remain campaign went with what had worked previously for them with the Scottish referendum, where they used a 'fear factor' to win and thought the tactic would carry over and would work again with the brexit vote.
They did have a significant lead in the opinion polls when they called the referendum, and there is a theory* that undecided voters normally stick with the mean (what they know) rather than vote for the unknown, so taking those two things into account, plus their experience of the Scottish Referendum they were confident of a win.
I think you are correct in what you said though.
*the theory has a 'name' - will try to find out/remember what the actual correct terminology is
There are probably a number of cognitive biases at play though that lean in favour of leaning. Firstly, and I count myself among their number, very few of us really understand the EU and how it truly impacts our life, so we resort to simplified heuristics that allow us to make emotional, snap judgements. Leave did this by suggesting that the EU were always deciding things on our behalf, and there was absolutely nothing we can do about it. It's twaddle, of course, but we see Pete roll it out even now, so it's been hugely effective.
Secondly, this version of events was largely believable because the media, and especially the tabloid media, have spent years blaming Brussels for all manner of things that have thus been 'imposed' upon Britain. This is why if you ask many people about the EU, bendy bananas are still cited with great regularity.
Thirdly, loss aversion was a major factor in the immigration argument. As I've mentioned before, there is a strong belief among social conservatives that immigrants and ethnic minorities (probably women too tbh) have taken status and power that was previously theirs, and that remaining in the EU would see this influence diminish even further. Couple this with the endowment effect that you see when people get all misty eyed about supposedly traditional British things, such as Rule Britannia, that the 'liberal elite' are trying to take away from them.
Chuck all those together and it really wasn't an economic decision at all, but rather a social decision that was centered around power, influence, and respect.
