Yes you are right Lars-Henrik as long as the owner of the aircarft is non-commercial DTO or Dry leased the aircraft from the private pilot-owner(s) and pilots are members of a non-commercial DTO, but they must comply with regulations regarding private-pilot(s) owner maintenance. In real life this can become quite complicated if they Dry lease the aircraft just for a short period of time. For such situations it is easier if the aircraft is in CAO.
The point in Costas question is wether the non-commercial DTO needs to own an aircraft for their training and the answer is no, as long as they have Dry lease agreemenet for the period in which they use the aircraft in their training and comply with all other regulations regarding non-commercial DTO and maintenance.
According to our experience, the best is, Short Term Dry lease agreement. This can be only for the time you really need the aircraft for training.