I disagree that having documentation will not help. Without documentation all you have is a statement that you did not damage the vehicle, while they hold the vehicle and all other documents. If you have photos and videos from when the vehicle was dropped off and picked up, then you become a much more difficult target for this shakedown.

I also have a strong suspicion that the Sixt staff must get a bonus or kickback based on the number or value of their damage claims. With that in mind, they would be encouraged to send you on your way thinking that you're in the clear and do not need to document.