Though the purpose of such exams is ostensibly different in  the first party (your insurance) versus the third party (the at-fault party),  the reality is the exams are conducted by the same types of entities with the same bias against soft tissue (musculoligamentous) neck and back injuries.

When the insurance company, in the first party stance, demands an exam, the plaintiff (injured party) should generally cooperate and attend in the accordance with the contract of insurance. However, safeguards should be insisted upon to the full extent as reasonably possible.  If the insurance policy allows for an "independent" medical exam, but the insurer is insisting upon a medical doctor who is biased, then letters show go out insisting on a different medical doctor. Also, sometimes, a legal motion known as a declaratory judgment action could be brought on the limited issue of the exam.  Due to the fact that litigation can be expensive, the plaintiff (injured party) in this example may ultimately be left with the choice between attending the exam, or declining the exam and having benefits terminated.  If the IME is to proceed, a letter should go out detailing to the insurance company the insisted parameters in regards to the exam.

When the case is in litigation (in court) and the defense requests the medical exam (IME), due consideration should be given.  California law allows the defense to examine the plaintiff one time prior to trial.