Thanks for all the replies... answering all questions below--
I didn't get a picture of the dumpster on my car since once I saw it, I immediately went to pull it back to see the damage. Have pictures of the dumpster close by, pictures of my door, and closeups of the dumpster paint where it hit.
I did get a police report and informed the dumpster company (private company not city department) of that-- when I told the guy on the phone, he wanted to try and get the operations manager to talk to me but the operations manager didn't want to get on the phone I guess.
Also, they haven't told me who the "end user" is. I've called and asked twice-- the guy even started saying that he wasn't sure whose dumpster it could be since it was in an alley. I told him that it was actually on the sidewalk on a busy street and funny enough, the picture of the dumpster with the same background of buildings was on their Facebook with a rock against one of the wheels holding it up! He kind of flustered and I could tell he was surprised that it was on their Facebook and said he would look into it.
I just came back from getting and estimate and they quoted a little over $2000-- needs a new door and to blend the paint. My copay is $1000.
Now, I am just waiting to hear back from the dumpster company before deciding if I will go through insurance. For me, its about the principle of the matter at this point. You can't just say you aren't liable and be dismissive when you have pictures on your Facebook with a ROCK holding back a dumpster.