If they damaged the door you are most certainly entitled to having the door repaired. I think having the entire car re-painted will not happen. You are entitled to try, of course. They will say something to the effect of "it's not our fault that your 11 year old car's bolt was so stuck that it went through the door in the process of removing it."
Give it a try, though! What's the risk? By comparison, and in too short a story, one of my neighbors was injured while working as a carpenter's assistant. After months of unsuccessful rehab, and several lobbying attempts on his part, the State is going to pick up the tab to re-train him as a designer. Unbelievable. Sometimes the magic works....