Sounds like the patient will have to sue their own insurance company. This isn't the first time this has happened and won't be the last. The patient needs to state very clearly that the PEER doctor didn't examine her and can not make medical decisions without seeing her. The insurance company can make her go to their doctor for an independent medical evaluation, and she must go.
Also, and this is VERY important. The chiros notes MUST be good. It can not be a check the box system. Notes should be transcribed (not handwritten unless they are VERY legible) and contain all the parts of PART or SOAP, they should be SIGNED for each date of service. The initial exam should be outlined specifically with findings and any x-ray or MRI reports should be included.
If the patient had previous back complaints, the chiro should only treat and bill the PI until the patient is back to where she was prior to the accident.
I'm sorry for your trouble, GEICO is usually very easy to deal with. But also understand that chiros notoriously overtreat and overbill when it's a PI since it's 100% money. (My husband is a chiro, so I'm not bashing all chiros, but you know who they are!)
So, basically, appeal from your end with GOOD documentation, and MAKE the patient be proactive with her insurance company. Otherwise she will have to pay your bill as she agreed.