It's hard to see it because of where the damages are and where the cameras are facing. I baby my car and wash it each weekend so I know all the scratches/damages on my car.
First clearcoat scratch on the left rear door is at 5:01 minutes. The guy has the towing rope in the hand pushing on the rear door.
2nd clearcoat scratch on the right rear door is at 7:24
Bottom paint scratch happened when they lift the front wheels onto the trolley using the metal bar at 8:31 or when they take it off at 18:36
Front lip scratches could have happened at 12:40 min & 13:22 when getting into the street or when getting into their business parking. Car go through an uneven surface.
Do you have photos from before showing that the damage wasn't there? That might help. If nothing else, you might try small claims to recover your deductible. If they learn they have to defend themselves in court, they might change their tune, or the judge might agree with your interpretation of the video.
Like Davewill said, what you know happened and what you can prove happened are different. You even put two times where the damage happened on the front lip. If you aren't even sure, how could a court find that damage was caused by them. Was it caused by them? Possibly. I absolutely believe you and your diligence with your car. However, does the preponderance of the evidence show that they caused any/all of the damage? I'm not so sure.