Moto Assist can tell when you're driving based on GPS, but there's also another clever way it can tell when you're in the car: the Bluetooth. You should be using a Bluetooth device for hands-free calling in the car, and realizing this, Motorola has included algorithms that will detect which bluetooth devices are connected while in Driving mode and will eventually turn on Driving based on the Bluetooth rather than GPS.
It's not something you'll notice immediately, as it take a few days for Motorola to analyze your habits and decide you have Bluetooth in your car. Driving mode on its own kicks on when you're above about 35 mph. And when you first get your Moto X, it kicks on multiple times during your drive. In fact, when I got my replacement X (2013), I was hyper-aware of this because the Tasker driving mode - triggered by Moto Assist's Driving mode - would bring up a pop-up every time Driving kicked on, four or five times during the drive to work. I very quickly disabled said pop-up until Moto Assist could relearn my car's Bluetooth.
If you haven't already been prompted to turn on this useful little tool, you can find it in in the Driving Section of Assist under More options. If you're not using Bluetooth in the car - and you really should - consider setting it up, or if you vehicle doesn't support it, you can easily pick-up a visor-mounted model like this Motorola speaker for Moto X geared toward Touchless Controls/Moto Voice.