I think it was more a deceleration of the vote towards leave. There's many parallels here, including the polls, to the Scottish Independence referendum, but the difference was that only one or two polls had put the Nats ahead, and then only a fortnight before the vote. The last weekend before the vote had all the polls showing in ahead or level. For just shy of a month now the polls have steadily shown Brexit @ the 45% mark, with Remain @ 40/41. That's pretty solid. Remain are looking for practically all undecideds to vote and to vote for them, and also some Brexits to defect. Brexit just has to get it's vote out.
Went to a Toby Carvery for Father's Day with my daughter, her boyf, the ex and her feller and the ex father in law yesterday. Only me and the daughter voting Remain. The ex (and she's a nurse) says she doesn't believe the £350m nonsense (but only after the daughter had demolished it before her eyes) but wants 'control of our borders'. Her feller has already voted and reads the Sun - lost cause. Doesn't even know the difference between EU immigration and non-EU immigration - reckons that poster of Farage prove that if they're in Slovenia (he originally thought it was in France) means they're now in the EU and can come here. Her father just kept saying 'There's too many in our schools and taking up the NHS'.
All three thought the economy might 'dip a little', but would pick up when we signed deals with Commonwealth countries like Australia and Canada. I hope Australia know that the Brexiters seem to be under the impression that they're going to buy everything that we produce from July onwards.
55/45 to Brexit. Sad, but that's my prediction.
Your story does not surrpise me. It must be replicated all over the country. Some had said the issue was far too complicated to be put to a general population (!) and in such a short time. I have read and heard some say they are scared of voting as they are scared of making the wrong decision (!).
As I said earlier, many people will vote on their gut feeling, on stuff they understand. The one thing that the Remain side should be winning hands down is the economic issue. Yet the Leave side is countering any economic information that the otehr side puts out as scaremongering. Without giving any data or stats of their own. Even when we have a dozen Nobel prize winning economists saying that Britain's economy will suffer after a Brexit, we still have the Leave side screaming scaremongering !!
I think it will be closer than you think. I am hoping that the bookies are right. (they rarely get things wrong, don't they?)
http://sports.ladbrokes.com/sports-central/uk-eu-referendum/



Not sure that'll actually be the case with the amount of contraband floating round LA