The point is they can't do it to all their clients.
Government can.
The bar for proving intent is very high. Its why most defamation suits fail.
> A public institution has to...
No, they don't have to do anything. Look at California. Specifically EDD and FTB. There are plenty of horror stories you can Google.
A public institution has to at least actually care about their public image or risk getting voted out, protested or picketed if it annoys sufficient amount of people, or sufficiently powerful people, in a democracy. A private one would just declare insolvency, restructure and rename, while still keeping the profits it achieved by "negative" bureaucratic actions.