More that Amazon can take away your books. Don't need to burn them, just remotely remove them.
Then more applicable advice seems like it could've been "Everyone should go to their Kindle library and download their ebooks as soon as they purchase them."
IIRC they can remove downloaded books. Better advice is "no non-free software in the house" and "mind your external dependencies" but that's a bit too extreme for most people.
They can remove books you download to your Kindle ereader, but they can't remove book files you download to your actual PC from the Kindle library.
Ironically, Amazon has previously deleted copies of 1984 their customers had already downloaded to their kindles and other devices.
I don't mean downloading to Kindle, but actually downloading the book file to your machine where it is no longer at Amazon's mercy. If the book has DRM Calibre takes care of that, it's how many people transfer Amazon bought books to other ereaders.
I'm not familiar with Calibre but AFIK, all kindle books have DRM.
It is a setting the author chooses when publishing their book through KDP, and some authors choose not to enable it. Pretty sure it is enabled by default though.