My impressions was that the corporate license was per user.

But when I try to register the license with the same user, using the offline license-key from the first set-up, I get an error message stating

Verification Failed
Unable to verify your registration details. Would you like...

No, the same email-address as I used for the setup on the first machine as it is for the same user.

But are you saying that the registered domain name for the license must be the UPN-name of the user in that AD?
We are using a private name space for the AD (and some machine setups are stand alone).

But the Registration Wizard says email and not UPN...