"Nevertheless, despite equality of rights, Australia does not have a national registered partnership or civil union scheme." 

 I think this sentence is misleading and should be removed, or at least be revised to show that there's no national registry for all relationships. Though, this would just leave "despite equality of rights", i.e. same-sex couples already have all the rights as married/un-married heterosexual couples. And I think this would remove the 'punch-line' the original author intended. Maybe the whole section needs to be revised. 

   tbarnes