You're wrong about Brexit, Pat.
The week before Jo Cox was murdered, the polls were 9-2 for Brexit. After she was killed it was 10-3 for Remain.
This shows that after the killing, people would lie to pollsters to pretend that they were supporters of evil killers.
https://en.wikipedia.org/wiki/Opinio...eferendum#2016
A bit like under Milliband, Lab was ahead. But he was behind Cameron on preferred choice for PM and Lab was behind on most trusted on the economy. As no opposition has ever won when behind on either of those metrics, it was clear that people were lying to pollsters over whether they'd vote for more austerity, but told the truth on whether they wanted Millibean or Dave as PM and who they trusted economically.
The US vote is similar. People not telling the truth that they intend to vote for evil.
Before and after Cox's murder, online polls were more pro-Brexit than telephone polls. Because people would be less likely to admit they were insular nationalists when they didn't have the anonymity that online polling confers.
Psephology is about more than the headline figures. You need to look at the background reasons that could be influencing the decisions.