Dave,
YES, I'm sorry to tell you that this is a scam, and a common one. I'm a frequent traveler and I haunt several travel-related message boards, and reports of this scam have been increasing among car rental agencies world-wide.
I was an almost-victim myself -- at a car rental agency in Auckland, New Zealand. The car they gave me had several scratches and minor dents on it, and I tried to get the agent to do an inspection and make note of the damage before I left, but he was "too busy" and assured me everything would be fine when I brought it back. Fortunately I had heard of this scam, and I took digital photos of the entire car, as well as the odometer, before I left the lot.
When I went to turn the car back in, the agent did an inspection and saw a decent-sized scratch on the trunk. He told me I was going to have to pay for the damage. I just laughed and told him to get his manager. The manager also insisted that I was going to have pay for it. I calmly dug out my camera and showed him the photos of the scratch, taken right before the shot of the odometer. You should have seen his face when he realized he'd been totally busted!
I NEVER rent a vehicle now without doing the following: 1) getting the agent to make a note on the contract before I leave the lot of ANY blemishes on the car, 2) taking photos myself of any blemishes, no matter how minor, and 3) getting an agent AT THE TIME OF CHECK-IN to inspect the car and make note on the contract that no damage exists, and 4) taking photos of the car to show there's no damage before I leave the lot.
It's often not possible to get them to do either #1 or #3. In those cases, you have a high likelihood that you will get a subsequent demand from them to pay for some damage that either already existed on the vehicle, or was done after you left. That's why the photos before and after are so important.
You do have recourse. Don't pay it. If they try to charge it to your credit card (and they might), dispute the charge with your credit card company. Keep in mind that it is incumbent on THEM to prove that you did the damage.
This scam often succeeds because people don't know their rights. If you refuse to pay it, they will eventually drop the case. They have no proof that you caused the damage...there is no chain of evidence connecting you to it. If they didn't note the damage on your contract AT THE TIME YOU DROPPED OFF THE CAR, with your signature showing that you agreed, then there is no way to connect you to it. It could have been caused by the next renter, or the guy driving the car on the lot.
Also, they most likely won't even fix the damage. They will bill you for it, then rent it to someone else, then try to bill THEM for it...and just keep all the money they rake in from it.
The only way we consumers can stop this scam is by not letting them get away with it.
Editing to add: kudos to your wife for hanging onto that car rental agreement that proved the damage was there before you took the car! Makes you wonder how many OTHER people they've tried to hit up for that bumper damage, doesn't? And how many have paid for it to be repaired? And yet it's still there...still being used to try to scam the next guy. It's a crime.