Thanks for your explanation, but honestly the whole interface is not very intuitive.
In some ways I think the interface should be improved, and is badly phrased, because what you call the "Welcome Email" is being used as the confirmation email.
I just disabled the Require confirmation parameter.
And now it works fine!
All new site users that create an account are automatically subscribed to the newsletter, receive the usual site creation confirmation, and DO NOT receive the Newsletter Welcome Email.
So that means what I want is possible after all.
At least that's my opinion.
My problem now is other - they cannot unsubscribe properly.
But I will leave that to the other forum post... :-)