1) you can't get your whole car painted when the damage is isolated to one part. You'll get a new door. let me re-phrase that. you'll get a door that fits & is of like kind & quality. That door will be painted to match the color of the rest of the car and the paint will be blended on the front fender & rear door or qtr-panel.
2) Insurance companies to not get rebates from body shops. That's illegal. We have fired lots of adjusters for accepting "rebates" from body shops. Most large insurance companies offer the person with the damage an incentive for choosing a body shop that is reputable AND reasonably priced. State Farm just started giving the person a lifetime guarantee on the parts & workmanship. My company has been doing that for 15+ years.
If you do not want to use the prefered shop then the adjuster that works for the company has a laptop that does the estimate. They write a check based on that estimate and don't give a damn what you actually pay for the repairs that are listed on their estimate. So don't go whining that the dealer is charging more than their estimate. Unless there are new parts, they do not care.
If you live in the sticks or the insurance company is small, then you get competetive estimates and they choose which one to pay.
If you want to get your entire car painted, talk to the body shop once you've gotten the estimate. Let 'em know you want to use their shop & see what kinda deal you can work out. My son scratched his name on the rear of my Expedition. When it was hit in the right front corner I asked and got the entire rear panel painted a no additional charge.
3) if you have uninsured motorist property damage and/or collision coverage you can file a claim. The rules that define an uninsured motorist vary by state. Since you have contact damage you should not have a problem in most states. I hope you filed a police report. Most states require "timely notification" to the "proper authorities" when a loss involves a hit-n-run.
Let me know where you're from & I'll tell you the rules for filing a UMPD claim for your state.
4) comprehensive coverage NEVER pays for damage caused by collision or upset by another vehicle.