Is the patient responsible for payment if their health insurance refuses to pay?

Yes. What the insurance covers is specific to each companies' plan. Depending on the plan your employer purchased, certain procedures may be covered. The best bet is to call the insurer to have them check into the benefit available for the procedure you want. If it is a customary procedure, you may have more luck if your physician writes a letter to the insurance company recommending it. Alternative medicine such as acupuncture and others, while they do often work, are on your own dime for most.