Currently, there are four choices for user self registration:

https://www.redmine.org/projects/redmine/wiki/RedmineRegister

disabled: users are not allowed to register
account activation by email: new users receive an email containing a link used to activate their accounts (users must provide a valid email address).
manual account activation (default): new users' accounts are created but need administrator approval. Administrators receive an email informing them that an account is pending their approval.
automatic account activation: new users can log in as soon as they have registered.

If the "manual" option is selected, the user can enter any email address but Redmine doesn't send any validation email to confirm that email address. The administrator approving the user account has to trust that the user entered their own email address.

Therefore, it would be useful to have an extra option: activation by email combined with manual approval. In this case, the user would enter an email address, Redmine would send the user a validation email, the user clicks the link in the email and only after they do so, the administrator can see that it is a confirmed email address and approve the account.