This sounds like the bumper bash I had some years back when both my and another car were reversing out of parking spaces and we nicked each other. I had a tiny ding at one end of my bumper - it was a very low-speed ding and I had actually stopped reversing already at the time of impact. The other car tried to claim a whole series of dings on the rear of their car were caused by the accident (this is the part that sounds the same) - absolutely no way that was consistent with what happened. I told them I wasn’t discussing it with them and insurance would handle it. ( Insurance sure wasn’t buying it and I even got my deductible back.)
Sounds like these people are trying blame a whole bunch of things on this - definitely let insurance handle it.