I seriously doubt any medical provider agreed to take less than full pay on such an injury course of treatment. A PT provider has a lien on settlement proceeds if you sue and recoup. That there is an offset from your insurance and copay does not absolve you from having to pay for the full cost of PT, in all instances I have ever seen.
If, on the other hand, you have it in writing signed by them and dated that the PT provider will take only what is collectible by them from insurance proceeds and your copay then you have a contract to enforce and defend against their current collection efforts.
Yet, I cannot imagine a PT provider would ever in a million years agree to take less than full payment. I have never seen that, ever and I have been doing this practice of law for over 25 years.
Good luck and I hope this helps you understand.
In order to participate in a particular insurance plan, medical providers will negotiate with health insurers and agree to take less than full payment for the privilege of being included in the health insurer's plan. Pursuant to the contract, the provided is usually precluded from seeking any excess payment from the patieint. You should first determine if the physical therapist was a participating provider. If so, you may be able to get your health insurer to remind the therapist about thier contractual obligations to the health insurer's members