Filming it is the right call. This way there can be no doubt as to what happened if someone is looking for the burger later, and they can get it comped by the restaurant without issue should they want another.
And with the whole table empty of people they had either already finished most of their meal/weren't that hungry, or it's a fake video.
Some cats are like this. I'd like to add a speech bubble to the last frame: "You may be leaking but I still trust you fully, I know you're safe and reliable. You always have my back, see?"