From this answer and the discussion in comments:
[T]he problem is mechanical damage: every time someone picks up a piece of fruit and puts it down again it may cause small soft spots and local damage - And think about the shoppers that try to judge ripeness by pushing or pinching the produce. This will cause damage, invisible at first, but rotting soon, either in the store or at other unsuspecting customers’ homes – Stephie
I had considered the harms of pushing or pinching the produce before this, and tried to avoid doing either, but hadn't thought of the damage from simply picking up something and putting it back down. And now that I think of it, I can't come up with a way to examine fruit without causing such mechanical damage. Even rolling it around in-place could be just as, or more, harmful.
What can I do to examine fruit without causing avoidable damage?
The first step is to only pick up items you're likely to buy. Then you only have to put down items that have an actual problem already.
For some things you want to check for ripeness, but under-ripe items are more robust, so it should be possible to pick them up gently without damage. After all, for its handled by people and machines quite a lot before you ever see it.