Usually, the police will make the assumption that you did not back up the car because this would be extremely unusual. If you have a manual however, and the car could potentially 'roll' back it is more plausable that you could have been going backwards.
The fact that the wife was the witness, is not particularly relevent because he could easly get her to lie about it.
If there was no damage to his car, and you live in a no-fault state you are probably in luck. In this case, I would not contact my insurance company at all. I would contact his insurance company to pay for the repair. Usually under no fault, your liability insurance will pay for damage to his car and his liability will pay for the damage to yours.
In a rear-end collision, it is not uncommon for there to be a situation in which no-fault doesn't apply. When this occurs, it is usually considered to be the rear car to be 100% at fault.
If you have not done so, DO NOT contact your insurance company regarding the accident. Contact his to demand the repair and let him worry about contacting yours if he thinks there is damage to his own vehicle.