I propose to have backup-by-copying-when-privileged-mismatch, which
preserves the ownership of files with low-uid owner (e.g., root-owned
system files), also preserve the ownership of files with low-gid group.

I think failing to look at the file's group was an oversight when we
implemented backup-by-copying-when-privileged-mismatch.  Are there any
objections to my fixing it now?

My proposed change is attached: