If it was not an emergency procedure and they became aware of the problem before the procedure was done, then yes--they should notify the patient. Otherwise, if the patient can establish that he or she only had the procedure done based in part on the doctor's claim that it would be covered, the patient may be able to hold the doctor liable for the cost (or at least for the additional cost over and above that portion or co-pay which the patient would have had to pay anyway).