BTW...the situation you are referencing is a stupid one. There are laws about that situation that seemingly the person who was hit didn't take advantage of.
The law says....when you hit someone then you are guilty. It doesn't matter what made you hit them. Its cut an dry.
That IS NOT a reason to file with your insurance company.
I guess I'll weigh in here. I'm an accident attorney in Southern California and deal with this kind of thing day in and day out.
First, you probably won't find an attorney to take your case unless there was bodily injury -- we typically don't take property damage only claims as it doesn't really work with our fee structure (1/3 of total recovery).
Second, there is no reason NOT to file with your insurance company. AAA has made it clear that they are standing behind their insured and are denying liability on this claim. There's no more working with them -- they are refusing to cover the accident. You have a few options at this point and none make sense except putting a claim in with your own insurance.
Option 1: You can fight AAA by hiring an attorney to fight your property damage claim (probably on an hourly basis as an attorney probably won't take the case on a contingency) and pay several times the value of the car pursuing your damage claim -- that isn't really a feasible option.
Option 2: You can take the Prius driver to small claim's court so that you are on equal footing (neither side allowed an attorney) but there's California law that allows the insurance company to simply set aside any small claims judgments against their insured's, which will then revert you back to Option 1 (having to go to Court against AAA -- not a feasible option).
Option 3: File a claim with your insurance. Pay your deductible (unless it is waived), and have your insurance fix your car for you. If you had to pay a deductible it will be refunded if your insurance is able to collect from AAA. There's no hassle with this option, provided you can pay your deductible. Your insurance fixes/replaces your car and there's no fight about liability. What happens in the background is that AAA and your insurance fight over who is the culpable party. If they can't agree on who is at fault, they will go to something called "inter-insurance arbitration." The two insurance companies essential have a mini-trial where they agree to be bound by the decision of an arbitrator. Your insurance will use your photos as well as any recorded statements to argue that the Prius caused the accident and there was no phantom third vehicle. When/if they are successful, they recover the money they paid to fix/replace your car from AAA and refund your deductible (if applicable).
As for diminution of value, if your insurance doesn't cover it, you likely won't recover it. Honestly though, from the photos, your car may just be written off so it is a moot point. I suppose you could sue the Prius driver in small claims for the diminution but, again, AAA can have any judgement set aside quite easily.
Do not waste any more time with AAA -- if they have denied your claim, there is really no practical way to go any further. The advice to avoid using your own insurance is very bad advice.