The applicant is Pilot in Command during a checkride, and the DPE is really acting as a passenger and likewise can only help the applicant with stuff that a non-pilot passenger could do. The DPE "passenger" could look for traffic, hold a chart or iPad or maybe grab something from the backseat. However, the DPE "passenger" can't help with operation of aircraft systems, look up approach plates, teach/coach or help you fly the airplane.
In the eyes of the FAA, DPEs are observers. They are observing your actions and how they comply with the ACS. There are a few checkride exclusions that do happen. For example, the DPE may fly the airplane when the applicant is putting on a view limiting device or maneuver the aircraft around traffic when you are under the hood but that's about it.
Anytime a DPE intervenes for safety of flight issues, the DPE has to issue a Notice of Disapproval. For example, extending the Flaps above Vfe, trying to take-off with full flaps extended or has to recover the aircraft from a messed up maneuver. The DPE also can not allow an applicant to break any regulations. Examples would be, flying into Class B, C, or D without authorization, allow you to bust VFR requirements or land without a clearance.