Good analogy.

I use all three, depending on the circumstances.

There have been times where I judged the error just needed to be fixed and nothing really needed to be said, so I did so.

There have been times where I felt a private communication (via whatever medium) was appropriate, so I did that.

And there have been times where I've called the person out publicly. I only resort to that when I feel that not doing so will cause more damage than doing so, or where I'm calling someone out for publicly berating another undeservedly.