I get why they might not be able to tell you how much you'll pay because of your specific insurer, but why would the overall price of the treatment change with it? That seems bizarre.
Its scummy and fraudulent, but issuing a large bill to an insurer, then getting a much smaller check back is how medical billing works here in the USA. Having your insurance pay for a trip to the ER after a car accident would be $7k for them, or $84k for your car insurance, hence why one should carry a car insurance policy with good driver/passenger injury coverage :P
Insurance should really be only high deductible plans, so the patient really looks into pricing for his general care/periodic care.