Earlier quoted context omitted.
You're correct. There's nothing about amp4email that requires a Gmail account. I'm actually pretty sure that if you use an imap client it whatever, you could view amp email from some site without ever communicating with a third party.
It would still need to talk to your email provider's AMP cache, presumably, though, unlike a normal email which you download once and then do not need to reach out to the server for again.
I could be wrong though, but I believe that works.