There are enough of these "seat reassignments" happening across most airlines that I wonder where the true problem lies. If Ms. Ann paid extra for her seat, how did that seat be granted to another deserving flier?
Bad programming somewhere in DL computers? Poor instructions to the staff? Unmerited overrides by staff? Not enough info to decide.
At some point it will fall back on poor management. That problems happen, no doubt. That peaceful resolutions can be difficult to manage, certainly.
But how an airline responds to a public criticism, in this day of universal cameras and social media, will prove to mean more to the long term health of a company than most anything else.
At least the company I used to work at had a pretty good PR department that seemed to never sleep ...