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Last tested: May 10, 2018
There are two different interpretations of this question, with two different answers.
1. On the Admin > User page, before editing a user.
If an email is grey here, it means the user can't log in with these credentials. In this example, SAML is enabled for the instance. User 538 is an Admin and thus is allowed to log in with Alternate Login using their email address. User 587, on the other hand, doesn't have the
login_special_email permission and is not an admin, so they cannot use their email address to log in, only SAML.
Two: On the Edit User page.
This means that the email can't be edited from here. When using SAML or another identity provider (IdP), Looker gets the email address from that IdP. You can't edit the email in Looker, because it will get overridden the next time someone logs in with SAML.