IDD Entity Registration is a separate level of security for dictionary entities.
The AUTHORITY FOR UPDATE clause on a USER definition indicates which entity types can be updated by the USER, but Entity Registration is another layer of security.
Each IDD Entity (ELEMENT, RECORD, MODULE, etc) can be defined with a PUBLIC ACCESS clause to restrict access to the specific entity, as well as a USER registration clause which assigns the authority to perform operations (MODIFY, REPLACE, DELETE, DISPLAY/PUNCH) for that specific entity.
If someone gets the DC601081 error when trying to update a particular entity, someone with the appropriate authority can signon to the dictionary in question and DISPLAY the entity to see how the PUBLIC ACCESS and USER registration clauses are defined for that entity.
Most likely you will see PUBLIC ACCESS IS ALLOWED FOR DISPLAY and one or more USER registration clauses indicating the USER(s) who are registered to be able to update the entity in question.
To resolve the problem with a particular user getting DC601081 for this entity, someone with the appropriate authority can either:
E.G. MODIFY entity-type entity-name VERSION nn INCLUDE USER username REGISTERED FOR ALL.
If the second option is used, the registered USER would also need the relevant AUTHORITY FOR UPDATE clause on their IDD USER definition.
After making these changes have the USER who received the error sign out of the dictionary and sign back in and retry the operation.