Ok, first off :
Insurance various state by state. Your coverage varies depending on what you decided to take in coverage. There is no FULL COVERAGE box to check to get everything, therefore you need to get your insurance agent to explain in detail what you are covered for - and if they say FULL COVERAGE and leave it at that, find another agent/company.
You are in CA, same as I am. Your Ford dealer may also be on your insurance companies list of approved repair centers. Mine was, and that is where my car was taken when I had an accident much like yours (the one before I bought this '12 focus). My insurance agent was called, who then had a claim agent take over, and I did nothing. They direct billed the rental company, and did everything and then they handled the other party's insurance for their expenses. I would let them do the work YOU have been paying them for.
Since my car at the time was a '07, they do, and will use "recovered" auto parts first, then new parts. When you are at a independent repair center, that means cheaper, third party parts. Since this was at Ford dealer, the new parts were from Ford. And they placed that in writing on my paperwork. And BTW - "recovered" auto parts mean they do a quick search in the area for wrecking yards to find a matching vehicle to "recover" those parts if undamaged.
As the woman in front of me that had no damage came back two months later with a $13,000 repair from her Mercedes Benz dealer for all the stuff under that plastic bumper cover. I referred her to my agent and never heard anything more about it.
Save all your paperwork, take notes, and pictures. Save it all.