I've never seen this happen before in all my rentals (probably 500+ in the last 8 years, 95% with Avis). Not saying it can't/doesn't happen as anyone can overcharge/double charge you, but it's definitely out of the norm.
Actually, the only time I've ever been double-charged for hotels/cars/airfare was a hotel 2 weeks ago. When I checked in at 9PM, I asked for a receipt because I'd be getting about a 2 hour "power nap" and then leaving and didn't want to be bothered going back to the desk. They somehow ran my card 2x.