I don't think insurance has any direct correlation to skill set. But, some PTs that are very good have a high patient load so they do not need to accept insurance that discounts their fees. But then again, some insurance programs are just a pain for providers to deal with so they drop them. Too much paperwork, slow pay, etc.

A physiatrist (Physical Medicine and Rehab) usually accepts many insurance programs. Maybe you can find one who is good with whiplash and concussions who could be a good start. Some osteopaths (DO's) are good. It is hit and miss.