The scenario where the furnace switch is turned off is not classified as a thermostat problem because it relates to a different aspect of the heating system operation. A thermostat is designed to control the temperature by regulating the heating system, but if the main switch of the furnace is turned off, the thermostat loses its ability to control the furnace since there is no power to the heating unit itself.
In contrast, faulty wiring, incorrect installation, and low battery conditions directly affect the thermostat's performance and its ability to communicate effectively with the heating system. For instance, faulty wiring can disrupt the electrical signals between the thermostat and the heater, incorrect installation might lead to the thermostat not responding correctly to temperature changes, and a low battery condition can prevent the thermostat from operating altogether. Each of these issues originates specifically from the thermostat or its immediate connections, unlike the status of the furnace switch.