Regarding who owns the past: I don’t think anyone can really “claim” the past, but I do think people who create their own ideas and research from the past can claim a degree of the past, but with limitations.
I copyrighted my site and basically said that as long as proper credit is given and permission is obtained, and licensed it under Creative Commons that said that sharing and adapting is fine, so long as attribution is given, it isn’t used for commercial purposes, and the ShareAlike license, which says that any adaptation must be done with the same license I used.
For my final project, I think I’ll license it with CC BY-NC-SA. That means that people can redistribute it (with permission), I must be attributed for my work, the work CANNOT be used commercially, the work can be modified and adapted, but the adaptations cannot be a diferrent license than what I licensed it under with Creative Commons.
While most of the works I intend to use for my project should be public domain, for more recent works (should I find them) may have specific licensing agreements. Most primary sources I have will probably be public domain paintings/movies/songs. I will still be vigilant in terms of what licensing is allowed for anything I do use, however.