We don't do a good enough job in communicating the difference unfortunately. But it is an important one. 

Yes, the Alby account is a managed account by Alby which requires an email to sign up. We want to make the first lightning experience as easy as possible until we have a non-custodial alternative ready.

But you can use the Alby browser extension in a completely self-sovereign way with your very own lightning node. Doing so you have full privacy with the Alby extension. All data is stored locally on your device.