Most people don't know / care. It seems only the technically inclined & paranoid lose sleep over this. Until somebody they know gets hit by identity theft, that is ...
The 'This website has not registered with Google' is only true for websites that haven't registered with Google - which mine has not.
It would go away for sites that have registered with Google - which I don't think would be too hard. Unfortunately, I couldn't find any sites that used Google authentication at all. I think this probably has something to do with the whole 'why bother supporting every proprietary identity scheme' thing.