He did the right thing by not taking any additional liability, the plane is on the ground safe..., he is done and so is his emergency authority by the way..! It doesn't matter that he has a type, he is certified on the right seat under the part, pilots have to be certified in both seats if they are to operate the airplane from either seat.
There is also another aspect to all of this, How is he going to switch seats? With the engines running? Most companies have very clear language on their operations manuals as to have a pilot at the controls at all times when the airplane is being operated, even is you set the parking brake if the engines are running that constitutes the airplane being operated...! He was very smart and professional in not doing any further operations with this airplane after he landed it safely.