Yeah, it's confusing. If your email provider is supported, your browser talks directly to your email provider, without Mozilla in the middle. We don't want your passwords, honest! :)
You can try out the supported email provider workflow by signing up for a dummy account at eyedee.me, and then using that account to sign in at, say, 123done.org.
Wait, if this system works with a dummy account, then a valid email address isn't necessary at all. Any domain can set up an identity provider to support user@domain. Why drag email providers into the discussion, then? It confuses everyone.
It confuses you because you are a technologist. For 99.99% of the world, user@domain == email address.
"Sign in with your email address" gets the point across. "Sign in with your user identity at a controlling DNS authority" may be more accurate, but will actually confuse everyone.
You can try out the supported email provider workflow by signing up for a dummy account at eyedee.me, and then using that account to sign in at, say, 123done.org.