I do not think that is true. How do you stay signed into google even though you restart a browser? There is a cookie that is stored and it authenticates you. When you first go to yt.com, it can ask google to authenticate you.. Call a url at google.com with a unique id and the response from that URL will tell yt if you are already signed in. The call to google can authenticate you since the call is coming from a google.com domain.

I am not sure if this is the exact mechanism.. but thinking that everything is origins, domains and websites and ignoring the fact that websites can call other websites (without making it obvious to the user) and they are all interconnected is a very naive assumption.