PD means you have no rights
No as in not a single right. CC0/PD means they can do anything legally: they can take the work, make a trivial edit and put their name on it [at least in addition] and you can't do anything. They can take the work, put a new cover on it, and put that work on amazon for 99.99 and using an ultra-restrictive other license. That's all covered under CC0:
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of his or her rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission. See Other Information below.
By putting something in the public domain, you give up all the rights you have to the work and simultaneously give everybody the right to do with the work however they please - including any changes and relicensing.
The only way to prevent this requires you not to use CC0 PD but instead a copyleft license that requires attribution. Such as CC-BY-SA.
But.... Author's Rights?
What I wrote above is true for the United States, but there are several countries that have a concept of un-sellable Author's rights - usually called moral rights. In those countries, claiming that someone else wrote the work isn't legally possible. Among those is germany, and the law there includes the right of attribution under the unwaiveable moral rights. Such laws are why I italicized a portion of the CC0 license deed: Not all countries allow you to give up all the rights, and the waiver is limited
to the extent allowed by law.
