du --count-links only counts hard-linked files multiple types. I assumed you had a symlink loop that rsync would have tried to unwrap.

For instance:

$ ls -l
foo -> ./bar
bar -> ./foo

If you tried to rsync that, you’d end up with the directories foo, bar, foo/bar, bar/foo, foo/bar/foo, bar/foo/bar, foo/bar/foo/bar, ad infinitum, in the target directory.