Obviously there's many exceptions. I don't want a doctor that just took a training course, but my doctor not taking american history or calculus? Not a deal breaker at all.
My sense is that's mainly true at companies where the founders/execs have prestigious degrees, and therefore put a lot of stock in them.
I think it's (unfortunately) quite helpful to these companies too, since appearances matter a lot. Telling a non-technical investor, prospect, or journalist "all our engineers are from Stanford/MIT/etc." will often impress them regardless of whether any of those engineers have a clue (something a non-technical person has no way to really evaluate).
But unless it's a household name university, I think you're right that it no longer matters at all.