This is incorrect. There are two systems here: autopilot and stall/overspeed protection. These are both automated systems, but they are controlled separately.

When autopilot is off, you'll still have stall/overspeed protection that will pitch down/up in the corresponding condition. This protection can also be disabled by switching off some flight computer control. This is the case for both Airbus and Boeing, and the specific controls required depend on the particular plane model.

The issue at hand is ensuring that training for these situations and knowledge of the flight control computers is adequate.