The thing is... on both the cited occasions (Nixon in 1968, Morrison in 2019), the politicians claiming the average voter agreed with them actually won that election

So, obviously their claims were at least partially true – because if they'd completely misjudged the average voter, they wouldn't have won

People vote for people they don't agree with.

When there are only two choices, and infinite issues, voters only have two choices: Vote for someone you don't agree with less, or vote for someone you quite hilariously imagine agrees with you.

EDIT: Not being cynical about voters. But about the centralization of parties, in number and operationally, as a steep barrier for voter choice.