you're not mistaken but it didn't say that on the ballot, it just said leave. That's the problem it was just so poorly thought out now everyone is trying to decide what "leave" actually means.But this would fail hard in the U.K., given that the leave campaign was fought almost entirely on immigration and this would require freedom of movement unless I'm mistaken.
we could "leave" and just be in an EEA type deal. That's leave. We could also leave and trade under WTO rules.
This is the problem nobody actually knows what to do so when we say leave it doesn't mean the same thing to people which is why Labour/SNP etc and Rees-Mogg/Boris/ERG currently find themselves on the same side of the argument against it but for very different reasons.