In Washington, few lines are as hackneyed as Sen. Daniel Patrick Moynihan’s aphorism that “everyone is entitled to his own opinion, but not his own facts.” That’s true, but it’s also true that pundits can sometimes twist a few “facts” into a false narrative. Consider three widely accepted misconceptions about the Democratic Party—each of them debunked by the outcome of the primaries to date.

First, those who see the party as a collection of self-interested identity groups get it wrong. Many assume that female candidates had...