Can't chmod or chown a file in TimeMachine backup directory
Reading up a bit on ACLs[1] I found that I could change ownership by first removing the file ACL with the following commands:

sudo chmod -a "everyone deny write,delete,append,writeattr,writeextattr,chown" problem_group_file.png
sudo chown :staff problem_group_file.png


After that the directory could be restored from TimeMachine backup without errors. This doesn't however explain why the problem occurred in the first place.