You're forgetting wear and tear. When the Yaris is moving, the gas is not the only being used, but so are the tires. And the brake pads and rotors. You're putting mileage on the odometer, spinning those wheel bearings, blasting the A/C, and maybe loosening up that CV joint more and more every time you turn left. Was that an exhaust leak I'm starting to hear?
With the moving truck, you don't care about that stuff, as it's baked into the rental cost. Even when the cost of the trailer is factored in you've saved money from wear. You still win.