Looking this up a little bit more, I think it's more complicated than I was saying but also than you're saying.
For the "normal" cases, you're right: you can have copyright on the original parts of a derived work. You are fully right though that the original work's author does not in any circumstance get the copyright for the derived work. That was a confusion on my part.
> But even if I were to violate the terms of the GPL (thus terminating my rights under the GPL), I still would not lose my copyright interest in the program I wrote, only my right to distribute it.
As far as I understand though, this is not true. If you were not authorized to use the original work, then even the original parts of your work are in fact not protected by copyright at all. So, if, say, I take a Spiderman comic and add an extra page of fanart at the end, without any authorization from Marvel/Disney, then my extra page of fanart is not protected by copyright at all, and anyone is free to copy it (unless it also infringes on Marvel/Disney's copyright of course) [0]:
> Only the owner of copyright in a work has the right to prepare, or to authorize someone else to create, an adaptation of that work. The owner of a copyright is generally the author or someone who has obtained the exclusive rights from the author. In any case where a copyrighted work is used without the permission of the copyright owner, copyright protection will not extend to any part of the work in which such material has been used unlawfully. The unauthorized adaptation of a work may constitute copyright infringement.
For the "normal" cases, you're right: you can have copyright on the original parts of a derived work. You are fully right though that the original work's author does not in any circumstance get the copyright for the derived work. That was a confusion on my part.
> But even if I were to violate the terms of the GPL (thus terminating my rights under the GPL), I still would not lose my copyright interest in the program I wrote, only my right to distribute it.
As far as I understand though, this is not true. If you were not authorized to use the original work, then even the original parts of your work are in fact not protected by copyright at all. So, if, say, I take a Spiderman comic and add an extra page of fanart at the end, without any authorization from Marvel/Disney, then my extra page of fanart is not protected by copyright at all, and anyone is free to copy it (unless it also infringes on Marvel/Disney's copyright of course) [0]:
> Only the owner of copyright in a work has the right to prepare, or to authorize someone else to create, an adaptation of that work. The owner of a copyright is generally the author or someone who has obtained the exclusive rights from the author. In any case where a copyrighted work is used without the permission of the copyright owner, copyright protection will not extend to any part of the work in which such material has been used unlawfully. The unauthorized adaptation of a work may constitute copyright infringement.
[0] https://copyright.gov/circs/circ14.pdf