There's a bit more involved than that though isn't there?
The Leave Camp were not in a position to promise anything, simply campaign. The referendum question said nothing of the single market or whatever, in fact I distinctly remember the options after leaving being very hazy. Boris himself was really dodgy in answering exactly what it meant for free movement. You voted for that, not everybody and I'm certain the close result would not have gone our way had it been a clear choice of a hard Brexit or none, more people would have been scared into the status quo.
People certainly did not