Does anyone actually know if employmemt references matter anymore?

I don't mean dates, salary, etc. Ive looked at my Work Number history. I mean, so many worry about the "reference". Will they say we are eligible for rehire, etc? Does that require an actual phone call with a real person, pulling your file, etc or is previous employment verification really all they care about?

Part of me thinks they've duped us into caring more about HOW we leave oir jobs and so we fear getting fired, but I am starting to wonder if automating hiring has taken the details out of the verification process. Anyone have actual insight on this?