Newsletter Signup CiviCRM Thinks Anonymous is Admin
Problem solved. What I had done was, in the "Advanced Settings" section of the profile's general settings, I had selected, "Add contact to Group" and then selected the mailing-list enabled Group I wanted to use on the form. This method totally circumvents the opt-in email.

What I have done since is leave that advanced section alone. Instead, I've added a field to the profile for "Group(s)." Now the opt-in email is sent.