This question presumes your claim is in litigation which would further mean you have hired your own lawyer (or I hope you have done so). So both sides are “lawyered up” as they like to say.
Now the insurance lawyer decides he/she is going to make a little private visit with your treating physician but plans to tell no one about it.
Your doctor (who might be an insurance doctor in his/her heart of hearts) still has the right to say NO. No private interview with me the doctor could say. A doctor may agree to be interviewed by an insurance lawyer in an ongoing case but only on the condition that either their own lawyer or more likely your lawyer has an opportunity to be present. If the insurance lawyer insists he/she want to record the interview, your lawyer has a right to have a copy of the interview.
Sometimes the doctor's staff sets the appointment with the insurance lawyer without putting much thought into the significance of what they are doing and how this event could hurt you, the injured person. Think about it. The insurance lawyer could say almost anything to the doctor about your past, about a non-existing criminal background, about a prior injury that never happened, in an attempt to influence the doctor to say something that is contrary to the truth or to anger the doctor.
I have found that if I ever suspect something like this is what is going to “go down” I will contact the doctor's office manager or coordinator of patient care and inform them that the doctor should NOT participate in such a meeting unless I am there.
There are a few insurance defense lawyers who are completely unscrupulous. When they enter the case defending the insurance company, I need to be “on my toes” and expect nothing but the worst to happen.
The Georgia Supreme Court weighed in on this issue in the case of Arby's Restaurant v. McRae.