The domain for my email is gmail.com not Aussie zone. I also cannot log in to gmail on the hotmail (outlook? )site. Perhaps you are interpreting their request to not use username and site name and instead use email, to instead use a long form Lemmy username?
That could work, but I don’t know that it adds any extra layer of simplicity, but maybe that’s what they meant. My interpretation is that they are saying to link your account to your email address, as that’s what most other services do. Without knowing which instance you register with, there would need to be a registry. Perhaps this could be hashed in some way, but it would still be effectively public facing as any instance would need access.