The cutoff is 75 miles, not 100, and the 1 mile thing sounds bogus too. This is directly from Avis.com EZFuelŪ and Fuel Service Charge
Driving under 75 miles? With our newest refueling service, customers who drive fewer than 75 miles pay a low flat fee for fuel and then return the car without stopping at the pump. Select this option and we'll automatically charge you a flat fee of $15.99, ($17.99 if you rent the vehicle in California). If you **FILL UP THE CAR*** AND present a receipt for your fuel purchase, the EZFuel charge will be removed when you return the car.
EZFuel option is not available at all locations. Please contact your renting location to confirm the availability of this service.