With a cellphone the GPS in the phone can - and will - track you six ways from Sunday unless you are very very careful, with a cellphone the carrier does not so much 'track your location' as that they record field strength to determine which tower you connect to as well as to manage the handover. To turn that into location data is absolutely possible but not nearly as accurate as GPS, especially not when you stop moving for a while.
Nevertheless, what you describe sounds a lot like a "smartphone with location services off" (assuming you trust the smartphone)