I am choosing peace.

Most of the time the choice is between peace and being right, and being right is enormously attractive. The evidence is all there. The other person is genuinely wrong about who said what in the car.

Winning it costs about four hours and buys nothing anybody would want. The alternative isn't pretending to agree; it's noticing that the transcript of a conversation from Tuesday was never the thing at stake, and letting it go unlitigated. Peace usually looks like an argument that simply didn't happen, which means nobody ever gets credit for it, including you.