Yes, a physician can require a patient to sign an arbitration agreement and, if the patient will not, can refuse treatment. There is no right to treatment by any given doctor; doctors are basically businesses, and can decide on the terms under which they will treat people (the same as they can decide whether to accept insurance and, if so, what insurance). They can also refuse to make a referal, the same way any business can refuse to refer to another business. The patient will have to find another doctor on his/her own.