I once ordered a lamp online - the entire lamp base was glass, and it was quite large, maybe 2 feet tall? So when the box arrived and it was bashed in on all sides, I took several pictures of the box and the process of opening the box, as I suspected the lamp inside would be damaged. I was correct - when I got the box open, thousands of shards of glass showered over my floor. Luckily I had thought to put a tarp down.
I contacted the store, attaching the photos, and they made arrangements to send me a new lamp. When they did, I asked them what they wanted me to do with the broken lamp's shade (which was shipped in a separate box and was undamaged), and I also asked whether they needed me to give UPS the shattered lamp and the damaged box for some sort of evidence. They responded that I should just keep the 2nd lampshade and throw away the shattered lamp and box.
So I did. And then two weeks later, I got an e-mail from UPS stating that they needed to come pick up the shattered lamp and the damaged box so they could "determine who was at-fault for the damages". This after I had already received my free replacement and the garbagemen had long ago picked up the damaged box! I told them as much and copied them on my previous correspondence where the company had told me to dispose of the damaged goods. They then asked whether I could contact my city garbage service and attempt to retrieve the box. Um, after two weeks? What state do you think it will be in, if it can be found at all, and how will that give you any sort of "evidence" as to the state it was in when I received it?! I gave them my best "that won't be possible".