London (CNN) Just when it looked like Hillary Clinton was going to make it through October without a nasty surprise, the FBI revealed it was reviving its investigation into her use of a private email server -- and suddenly her healthy lead in the polls began to wobble.

But is it enough to give Donald Trump hope of capturing the White House on November 8?

If you're watching the polls, you might doubt the email scandal will change the race.

Clinton is up by five points nationally in the latest CNN/ORC poll, and by the same margin in CNN's poll of polls, even after the FBI announcement.

One Irish betting site thinks Trump is so sure to lose that it paid out $1.1 million to people who gambled on Clinton three weeks before Election Day.

If Trump were a traditional politician, he'd be telling supporters about now that the only poll that matters is the one on Election Day.

In fact, Trump has been telling supporters the polls are "rigged."

They're not.

But what if the polls are simply wrong?

Brexit surprise

One vocal Trump ally says pollsters get things wrong -- and he has personal experience to prove it.

Nigel Farage was one of the loudest voices campaigning for Britain to leave the European Union in the crucial national referendum held in the United Kingdom in June.

His side won the vote on "Brexit" to the surprise of much of the world. (The site that already paid out on a Clinton victory said there was only a 10% chance of the pro-Brexit side winning.)

"On the day of the vote, there was an opinion poll that put us 10 points behind, but we won," Farage claimed in an interview with CNN's Brooke Baldwin.

The polls were wrong because people who don't usually vote turned out, Farage argued.

"Modern polling companies cannot get to non-voters who are re-entering the system. The question is, is Trump reaching non-voters? I'm told that new registration of voters is quite high. It could be that Hillary's ahead, but maybe by not so much."

Big enough lead for Hillary?

Unfortunately for Trump, Farage doesn't quite have his facts right.

John Curtice, the dean of British polling, said Brexit surveys were actually pretty accurate.

"In the end, the average of the opinion polls was 51-52% for Remain, but we had some putting Leave ahead, and the Internet polls said it was a 50-50 shot from the beginning," Curtice said.

The vote turned out to be 51.9% for Leave to 48.1% for Remain.

"The polls in the UK, we can say, were 2 or 3 points out, but you wouldn't want to say more than that," Curtice added.

Trump is not polling that close to Clinton, at least in the immediate aftermath of the renewed FBI interest in her email server.

But there have been two British polling humiliations in recent memory, with errors big enough for Trump to draw comfort from, Curtice conceded.

"There are certainly historical precedents in the UK: 1992 (and) 2015, where the average error of the polls is roughly 7-8 points, the kind of lead that Hillary currently has in the polls," he said.

"So, sure, if anybody has any sense, you wouldn't want to say that Trump's chances are zero."

And Curtice said Farage may have something else right: British pollsters may have failed to pick up people who don't normally vote but did show up to vote Leave in June.

"We don't have the data," he said. But "if Trump does get the people who don't normally turn out to vote, who don't normally get called by the pollsters, then the polls may be wrong."

The art of polling

That's because polling is not just number-crunching, said Robert P. Jones, the head of PRRI, a Washington-based opinion research organization.

"It is some part art as well as science," he said. "We have to start modeling 'likely voters.' You have got to make some judgments: Is the electorate like 2008 or 2012?"

Farage has argued that some Trump supporters may be embarrassed to say they are backing him, which would mess with the pollsters' models.

"Maybe also people aren't telling pollsters the truth. Thinking, I don't want to tell a pollster I'm voting for Trump, but in private, that's how I feel and that's what I'm going to do," he said.

Steve Hilton, who was a political strategist for former British Prime Minister David Cameron, thinks that's very possible.

"There is highly likely to be a secret Trump supporter phenomenon. I don't think it's possible to estimate how many, and polls will by definition not pick them up," said Hilton, who is now the chief executive of political crowdfunding and data site Crowdpac.

He sees a parallel between "the widespread moral shaming directed at Brexit supporters there and Trump supporters here, most obviously seen in Hillary Clinton's 'basket of deplorables' speech, which mirrored accusations in the UK that Brexit supporters were racist, xenophobic, bigots and so on."

There is no way to predict how much impact they will have, if they exist, Hilton said.

"I think it's unlikely that the secret Trump supporters are numerous enough to sway the entire election, but in tight races in places like Ohio and possibly even Michigan, they could deliver a real surprise next week," he said.

What's socially acceptable?

But Jones, the opinion pollster, doubted there is a mass of secret Trump voters.

Pollsters know that people are more likely to give socially acceptable answers when they're contacted in a telephone survey -- there's even a name for the phenomenon.

It's called the Bradley Effect, after Tom Bradley, an African-American candidate for governor of California in 1982. Polls incorrectly predicted he would win.

Looking back, experts think that's because at least some people told pollsters they would vote for Bradley, even though they didn't plan to, in order to avoid sounding racist.

Internet polling can help control for such misdirection, Jones said, because people who fill out online surveys don't have to interact with a live person.

"There is no evidence that there are secret Trump voters who are systematically lying to pollsters because they believe it is socially unacceptable to tell a live interviewer they are supporting him," Jones said

"This fall, PRRI conducted both self-administered online polls and live interviewer telephone polls and we saw no significant differences. So I see no evidence of secret Trump voters who are simply reluctant to admit they are voting for Trump."

In fact, the only firm data available at the moment -- early voting statistics -- suggest that the Democrats, not the Republicans, have the advantage nationwide.

But in the end, Curtice said, the politicians' cliché about unfavorable polls is true: "The only way to find out is on the day itself."