[Standard Ebooks](https://standardebooks.org/) has accomplished a lot in producing better ebooks of public domain texts.
Public domain obviously can be ascertained, but if CC0 hasn’t been granted we rely on dated reproductions: basically a photograph of the artwork in question in a book or journal with a copyright date of 1924 or earlier.
(that’s obviously specifically a US legal reading, but SE from a legal point of view is a US project)
The difference between falsely claiming something is public domain and falsely claiming to grant a license to it under CC0 is going to be pretty minimal (and is likely result in little more than "please stop", blood and turnips and so on).