Wait, seriously?
I broke my arm late last year in NYC pretty badly, ended up having to get a surgery for carpal tunnel release + a titanium plate implanted.
Doctor told me I needed to do physical therapy for a few months after the surgery (which made perfect sense, because I could barely move/rotate my wrist, no finger/grip strength, and my mobility range was abysmal).
I searched for a reputable PT place nearby that was accepting new patients and that was a member of the American Society of Hand Therapists (per my doctor's recommendation), scheduled an appointment for the week after, gave them my employer's insurance info, and that was it. I never had to interact with the insurance company throughout the entire process, and they covered it just fine.
I know it is anecdotal, but out of my friends who deal with PT way more often than me (typically those who are seriously into competitive team sports), I am yet to hear of a differing experience either.