Anonymous tarballs

What I was missing was --group=root in addition to --owner=root.

tar -c --{owner,group}=root

(possibly with an optional --numeric-owner) fully anonymizes the archive.

You can use --numeric-owner, that will just put your UID (1000 or something similar on most systems) in the file. From man tar:

 --numeric-owner
       always use numbers for user/group names