Drupal assuming admin created user, when user registered normally
As it turns out, a custom-made module conflicted with the normal behavior in a sneaky way. 

In D7, when you create a user as an admin, the checkbox to send an email with a one-time login link is not selected by default. As the person creating users is not a technical person, I thought it might be user friendly if this was checked by default.

After a bit of searching, I found a small module that could help. What this piece of code did was:

if ($form_id == 'user_register_form') {
    $form['account']['notify']['#default_value'] = TRUE;
}


However, as you can see there is no check if the current user is the admin. So Drupal assumes the admin is creating the user, even for a normal registration by a visitor. Subsequently, the visitor gets a mail that the admin created his/her account.

I explained this for the author also, and hope someone fixes it (or I'll try myself when I find the time).