Can I force get my Health Insurance to pay for an MRI they deemed not "medically necessary" if it showed a major injury?

Age: 35 Income: Formerly $103k/yr now none State: Washington

The title basically says it all but I will add a little context. I injured my shoulder in the climbing gym in early June. After seeing my primary care physician he did some rudimentary tests and said he didn’t think it was anything serious, but told me to monitor it and wrote me a prescription for physical therapy. After going to a physical therapist (which took an entire month to find an in network PT and get and appointment) he did more comprehensive movement tests and determined that I had a torn tendon and / or labrum. The PT recommended I get my shoulder imaged to confirm his diagnosis. He also mentioned the odds of recovering from this injury with only PT were mixed at best and implied I may need surgery in the future.

So I went back to my PCP who requested an MRI which he ordered at another medical facility. Sure enough the day before the MRI is scheduled I get a call saying I have to reschedule because the procedure hasn’t been pre-approved by my insurance company. I followed up with the insurance company and got the vague answer that they don’t deem the MRI to be medically necessary despite the fact I have seen no decrease in pain for 2 months and my PT thinks there is a serious injury. At this point I’ve already been injured for 2+ months and can’t do most physical activities and have gotten no medical help I’m also tired of my insurance companies BS (they have done this before). So I called the MRI place back and told them to keep the appointment and that I’d just pay out of pocket. Which is what I did.

Now that I have the MRI and radiologists report that definitively shows I have 2 partially torn tendons and a torn labrum is that sufficient justification to prove this imagining procedure was “Medically Necessary”. If not, why not? Can I submit a claim to them for the MRI and force then them to pay?